. a, b, c, d,... gab R. g ab

! " #$% #&'( )*+,',-, / " 234 24445 6 78! 9 :!#7,'7 ;<=>?=@=A @B= C DB EE= DB EBF; FD ;CDCG H =DF CG AFD = ;=> C DB ID= D=CH= DC =DDFI @ D H C CHDF ;=CD JF DBD DB= ;K=>= ;D=; L> D> DDC=F ;==CDK;==FCG ;;D= @ D H DBD DB= = EED ;B=G C EED > H M= E JDB ;==CD DB ;B=G = C=CD ;B=G@ NF J=>O ;=CD CGDB P ;==CD P ;D=; L> ;B=G @ Q *R #!,T +U 7R 9V ',+ W 7*,'X 9V ',+ W 7! ##X,# 7 7Y 7V '*,# X! +T 7#Y+ 7* #*WV 7 %'* # -*'#* #,T,Y # Y'WW U! +!& 7* '* U * *,! 7W',V Z @ [ C\J \ ]^ _ ` C DB =;CD EE= bc B BJC DBD > D DB H CD >d=c; ADJC DB D= D=CH= DC ef DB EE=CD D=CH= DC eg f e bc hcf C ;C E\ AD DJ H= H =DDF O DB I =DDFI DB Ig =DDF@I B I =DDFPI JB;B ;=CD H=DC H =DDFP A> C DB H EBF; MCDD ik> CC eij f E;D DC=P @ @P C DB ;=CD >LCDC H DB E;D CGDB P DB ;=CD ;D=>FC ; JDB ik;d= E α B α bc kc@ B H=DC H ;D=>FC ;, MCD D DB ;=CD ;D=>FC ; JDB DB ;D= GCD; L> DC= F αβ P BJC C bc@ T 7!,T,!7*+ #!X 7,'#*+ # mn +U 7R,'X, *+#!+!!!'*8,#,T +7X o-7*,',v p'* mn +U 7R,'X q R#*+'! '* 'r! *, '*!,'7W!7X + #!! *R p)st +q #! '* 'r! *, R##!'*7,'u7,'#*+ # +#X )st B > ;CH= JDB DB E; =DDF DB DB=F H ij E;D JDB E>Kv;>C G D=FP @ @P DBF DB CD= DB DB G D=F H E;D C;BCG> @ gc w E H DB = DB =CD D=CH= ds DC e f H ij DC= MCDD@ B Ig =DDFI DB ;CCDC E; =DDF A> C vcdc y =DDF H DCDF C > C DB FC;B=C >LCDC H DB ED CGDB P @ @P C DB g H DB ED CGDB edb =CD ;CD=;DC P bp h P k P icf DB D >DC; edb ;CCDC >DDC H D fp P BJ C C bc e kcf P C DB g H DB ;D=; GCD; DB=K;D= ekk;d=f edb ;CCDC D=CH= DC H f@ T z 7! E B E B *#,,T,!7*+ #!X 7,'#*+ # mn +U 7R,'X, *+#!+ 7*,T V # *#,!!,#,T +7X o-7*,',v p'* mn +U 7R,'X q 9-, 8,T V!!,#,T +7X X 7+-! X *, '* 'r! *, )st + C DB EE= J CDGD EBF; FD ;CDCG H =DF CG AFD P D ;==CDK;==FCG ;C >;D= e{{{ fp CG ;=CD H= DC H EBF; MCDD EBF; EBC C P @ @P DB I =DDFI @ =D J w C DB ;=CD >LCDC H CGDB JBC >L C G D=; D= C >d=cd ;=>CDDC H C @ } =E=D C we=c H= DB =CD D=CH= DC P J B;B E CD H DB ;BC FC;B=CDC P @ @P ;=>CDDC H C @ =DB= P DB g H DB ED CGDB K DB =CD ;CD=;DC K w C >D@ BC DB ;=CD >LCDC H CGDB C vcdc y ;=>CDDC EE> D DB ;=DC H DB JK\CJC I=DD;I E=>w I{= G=G E=>w @I D H DBD C DB I =DDFI P ' #* Y 7*,+,#!,7'*,T R#** R,'#* Y',T,T U!! W7,'&'+,'R U TV+'R+ '* YT'RT #* 7W+ Y',T,T ~+U 7,'7W W *8,T ~P DBC CF DB =D CGDB e f H DB A?;D J >L M CDDF@ = DB =D DB ;=CD >LCDC H ;B=G J L DBD C DB I =DDFI DB ;B=G >CDF DB DB=K> CC ekj f MCDDF B >LCD EBF; CCG CF H= b

;B=G D =D @ C =>= D > H= DB AGCCCG DB =DCG H DB I =DK DFI H = ;B; H DB =D H= H DB A?;D P DB D=DCG H= H= DB >LCDC H ij MCDDP J EB DBD DB I =DDFI ;=CD C DB C @ )*,T ~! W7,'&',V ~ #* R7* * mn U TV+'R7W o-7*,',' + 7* '*& +,'8 7, U TV+'R7W W7Y+ R#** R,'*8 +-RT mn o-7*,',' + '* 7*V )st *#, #*WV '*,T! +,!7X #,T #9 R, T Y'WW R#!! R,WV R#** R,,T! +-W,+ # X 7+-! X *,+ #,T +7X mn o -7*,',V '*,Y # 7!9',!7!V! W7,'& WV X #&'*8 )st + BP DB I =DDFI > CD E=H==> =H=C; H= @ = ;B; H DB =D H= H DB A?;D > CD C C CF JF DBD DB H= E=H==> @ B =D H= P C H;D P DB D ;CCCD H= DB E=E H ; E=C JDB DB E==DD; EBF;P C JB;B C > CD > JDB ij MCDD AD JDB Ik bi MCDD edb MCDD >L C Ik bi E; D fp JDB DB Ig =DDFI P C JB;B C J=\ C ij E;D AD JDB MCDDP @G @P DB ED CGDB P DB D >DC; P DB kk;d= D;^ DBD = CD ij DC= MCDD@ \CG DB CD ;;CD J BJ DBD DB ;==CD >CDF ik;d= j H= {{{ C C =AD==F >D= DB j + + P JB= DB ;==CD >CDF ik;d= j j + j H= ED CGD ;B=GP =E;DFP B D A H C DB= JC =D H= P DBC D=CH= > AF DB =CD D=CH= DC D DB ;=> @ BC C ;@k @h J MD DB ;=CD [ wj MDC JBC J=DDC AF DB ;D= GCD; L> DC= F αβ AF DB ik;d= E α B α eadb H= J= =>F H C bcfp J =E=D CJ H= K DB, ;=CD [?=C H= H [ wjy MDC@ BC DB ik;d= E α α = >D= B H= {{{ ecd> H DB kk;d= D AD C ;B ;=CD JFP @ @P C DB I =DDFI P DBD P H= DB A== E D B) =D C DB =D H= H DBD {{{ P DB= ;K=>= ;D=; L> D> DDC =F ;C >;D= J DB D>F ;==CD @ ;B L> = =>F DB=D;F E=>;D> C >d =CD G= C c P c@ C ;CD=D D E= J=\ J L C ;B ;=CD CC= DBD DB= = EED ;B=G C EED > H M= E JDB ;==CD DB ;B=G = =CD C=CD ;B=G@ C DB EE=;B P @ @P C DB Ig =DDFI P D H DBD DB= C ;D=; CD H= CG E JDB ;==CD @ ZJ= J L DBD ;B E P =G=>CG DB ;D=; d;dp JF P AB D CG >DC; C ;D=; M>=E @ ^ ` _ ` _ g >;> C bcp e kcf ;;=>CG D DB I >=CI ECD H J DB E; =DDF DB DB=F H ij E;D JDB E>Kv;>C G D=F@ CDD H EBF; CD=D P ADB ; CC;P = =E=CD> C DB E; =DDF AF E;D DC=P @ @P ;=CD MCDDP DB J H EBF; = J=DDC C CHDF ;=CD JF DC= MDC@ B G D=F H DB E;D GC=F >L AF DB C=CD CLCD E;D >DC; ds H DJ CGBA=CG ECDP ds 2 = d g b d b >ED DB HJCG ;CCDC JDB =G=> D ;@ ED> ; EF DC @ DC ; = D A => ;;=>CG D, b, c, d, DB AD=;D w CDDC P cp ; @h @i @@ BF >GCD G D=; A?;D DBF =C H= D k @ B d,b g b, H ;= = >L ECDF H CF ;=>CD FD P ds, @G @P ;K=C\ ;=CD DC= ejb CC ;=D= DC= gb R =FJB= CBCG DB E;D H E; =DDF D E;D P DB >LCDC bcd C;> CD CF DB AD DB ;;=D> H= H =H=C;f@ =\ ; =C H= D k P JB DC ; =C H= b D k P DBF ADB >GCD DB ; ECCD H G D=; A?;D C i, j, ;=>CD k,, ;B=D P @G @P (, i ) (, i = DJ ;=>CD =E=CDDC ) H DB EDC ik;d= C DJ >d=cd C=D ;=>CD FD, DB g ν 4 4 D=w H ; ECCD H C ;=>CD ;B=D @ g b ^]^ C GC=P C ij E;D H E; =DDF D CD EA D E=D DB ED h

D E= E=D H ds P = ;;=>CG D [ C\J \y J=>P MD> B= DD P,T + U 7,'7W 7*, XU #!7W U 7!,+,7% * + U 7!7, WV W##+,T '! U T V+'R7W X 7*'*8@ B=H= P CF DB C=CD E;D CGDB edb =CD ;=f A DJC DJ E CD ecdf C ij E;D > B >LCD EBF; CCG C DB I =DDFI D >L = ( g b b ) /2 ebf, JB= ( b ) DB >DC; ik;d= ADJC DJ CD A B P = B P A = DB EDC ik;d=p DB D=; DC= @ A,B gb CG >d=cd ;=>CDDC H GC =H=C; H= P JB;B ;C A => P H= w E P AF C H >d =CD FC;B=CDC P J L >d=cd we=c P @ @P >d=cd =E=CDDC H DB E;D CGDB v M @ebf@ AF DB ;=>CD, H C CD P JBC J=DDC C ;=>CDDC H C P > CD B C CD=C; CCG C ij E;D @ ZJ= DB E;D CGDB ebf > B DB H= =DF CG C=D ;=>CD FD D =E=CD C CD=C; HD= H DB E;D @ jd=cd FC;B=CDC = >D= AF DB E= D= C DB =DC ε t2 = t +ε(t 3 t ) P JB= = DB D H >E=D= ==P =E;DFP H DB GBD GCP => AF DB t t3 ;;\ D P DB D H =;DC D P => AF DB ;;\ D P DBD B D A FC;B= JDB DB A ;;\ D t2 @ F EBF;D E=H= B vcdc y FC;B=CDC B ;CCDC JDB A ε = /2 C JB;B DB => ;=>CD ;DF H GBD edb CKJF E> H GBDf ;CDCD D=E; @ g C; w E H CCKD=> FC;B=CDC I=F>FI ;;\ FC;B=CDC c C JB;B DB= C AD DCDF c H= C AD DCDF ε = C DB E ; =DDFP H= DB =J C FC;B=CDC DD DB= DB =;CD =D; bc@ g we C co I = H J D=C C DB => D = ;;\ AF DB D=> CCC; CD I @@@D DB H DB D DC P D J A bh y;;\i P DBC J B FC;B= = ;;\ JDB DB D> ;;\ C CC= DBD ;==E D D\CG C } BC vcdc y FC;B=CDC H >DCD ;;\ ;=DC E; ε = ;=>CD t2 = t +ε(t 3 t ) i = > C C edb ;=>CDDC J A C > vcdc y = II ;=>CDDCf DBC e P @G @P DB G D=; A?;D =E=CD> AF DB D=w H ; ECCD H C DBD ;=>CD ;B=D P @ @P D DB gb [ C\J \ D=; DC= 4 4 JB= II gb D H= vcdc y gνe = dig(,,, ), ;=>CDDC @ } DB ;B DB E; gνe i D e te ( e ct e ) ; ECCD H > B DB= CCG @ BC e ds 2 ;C A J=DDC JDB DB E=D> ED D E= E=DP ds 2 = (d i e d ie) (d P DB BEEC JDB DB E;D CGDB e )2 ebf, 2 = ( ;B E=DC = C > C DB= C=D ; =>CD FD J DB DB [ C\Je i \ ie) ( D=; e )2@ DC= P C C L 2 = ( e i ie ) ( e )2, JB= e C ;CC;D> JDB e C AF DB @ C DB H= DB ;CC;D DJ ;=>CD =E=CDDC ec DB II ;=>CDDCf e, H GC CD @ e e, =H= D DJ =DF CG ejdb DB [ C\J \ D=; DC=f e, e = L ν,e ν e, L,e = γ e, L i,e = L i,e = γ e V i e /c, L i j,e = δ i j + (γ e )V i e V je /V 2 e, JB= V i e = d i e /dt = DB ; ECCD H DB =>C=F ;DF kk;d= P e γe ( Ve 2/c2 ) g we C bbc P J BC ;B =E=CDDC H E= =CD D=CH= DC = /2@ EK E> D ;=CD we=c DBF >D=F DB ;=CD H= O IA ; DBF EF DB=K ;D= CDDC P A ; DBF D=D DB ED D E = ; E CCD E=DFP A K ; DBF = E= D=> AF DB =>C=F ;DF DB=K;D= I C =>= D ADC ;K V =CD we=c H= L DB =>C=F ;DF =E;> C bbc AF DB E=E= ;DF ik;d= ν,e v e d e /dτ = (γ ec, γ e v i e ), dτ dt e/γ e DB ;= E=E=KD P DB CD ;D= n e (,,, ) CG DB D E= w CD=>;> P δ i j =E;> JDB DB [ C\J \ D=; DC= g νe B BJ DBD DB ;=DC E; ;=>CD i e vcdc y FC;B=CDC H >DCD ;;\ = we;df ;BC C bbc@ C ;B JF DB ;=CD we=c H= L ν,e C DB II ;=>CK DDC H C bbcp vm @e fp L ν,e L ν,e(v) = g νe 2n e v νe c + (n e + v e /c)(n νe + v νe /c) n e v e /c k

C; J JCD D DB C >d=cd ;=>CDDC J GC= DB we=c H= L ν,e H= bbc L L b L b(v) = g b 2n v b c + (n + v /c)(n b + v b /c) n v/c ;B H= ehf H DB ;C A EE> D C =AD==F C=D ;=>CD FD C JB;B DB D=; DC= ;C A >d=cd DBC DB [ C\J \ D=; DC=P DB DB H= H DB ;=CD ij =CD D=CH= DC ehf ECD H DB ;BC FC;B=CDC P @ @P ;=>CDDC H =H=C; H= @ D J B D CD DBD n C ehf E;L; MCDDF@ F D JF B D A D\C DB CD ;D= CG DB D E = w C DB ;BC DB ;BC ;=>CDDC @ =DB L ;==;DF D=CH= ij DC= MCDDF H= C D CDB= =DF CG @ = b w E P JBC L EE> D DB EDC ik;d= b C L ec DB AD=;D w CDDCf ehf = + [n (2γ + )v /c] n + (n + v /c)v /c n v/c ekf D w C DB =DC ehf ekf C DJ >d =CD ; =>C DDC@ =D C DB II ;=>CDDC P C JB;B DB [ C\J \ D=; DC= > P n A; n e (,,, ), 2 C LP v e = (γ ec, γ e ve i), γ e = n e v e/c, C bbc@ = DB GC= =DC v v = c C DB II ;=>CDDC P DBD v e = (c 2 + ve iv ie) /2, JB;B BJ DBD DB we=c H= L ν,e E= D=> CDF AF DB DB= ED ; ECCD v i H DB E=E= ;DF ik;d= e v e BC P CG DB A we=c H= n e, v e, C L H= ehf ekf DB we=c γ e H= E= P C bbcp @ @P DB A CD L ν,e P AD JDB e v i =E;CG DB ; ECCD H DB =>C=F ;DF kk;d= g P J L DB A CD e we=c C DB II V ;=>CDDC H= ds 2 = ds 2 e = (di e d ie) (d e )2 2 = e 2 = (i e ie) (e JDB DB E=D> )2, ED D E= E=D@ C DB = JF J DB =DC ehf ekf D J=D DB ;==ECG we=c C CDB= ;=>CDDC P I=I ;=>CDDC P H C P JB;B H C cp JB= I=F>FI = I=>I FC;B=CDC H >DCD ;;\ > @ = E;DF J ;= hj E;D ( ) C c@ BC DB D=; DC= A; JB= I=I D H= I=>I gb gνr =, ed >d= H= DBD C C c C; DB [ C\J \ DC= = >d=cdf@ B L C DB I=I ;=>CDDC ;C A F H H= ehfp H= DB \CJC ν,r gνr, JDB n r = (, ) γ r = n r v r/c = γ e B =DC ;C A H C cp = AF C H DB D=w T JB;B GC AJ @ B DB E= =CD D=CH= DC D=w ν, L ehf A; C DB I=I ; =>C DDC b ( ) K L ν,r = g J L DB I=I =E=CDDC r β r /K /K H ekfp r = K r, r = (/K)( β r r + r ), JB= K = (+2βr ) /2 β r = d r/d DB ;DF H DB H= r => AF DB H= =DB= ds 2 = d g b d b A; C DB I=I ;=>CDDC ds 2 = ds 2 r = [ (d r )2 + 2d r r] d } DBD C DB I=I ;=>CDDC DB ED D E= E=D H ds 2 = CD E=D> P DBD >d=cd DBC C DB ;=>CDDC JDB DB [ C\J \ D=; DC= @ B B> H= DB E;D CGDB JB;B C DB I=I ;=>CDDC >D=, 2 = r 2 = [ ] (r )2 + 2r r vwe=cg d r, = r P C D= H d e, = e edb D=CH= DC D=w A DJC I=I II ; =>C DDC ( ) T ν =, JBC; P @G @P r = e e, r = e, β r = β e /( β e ), cf C L DBD ds 2 r = ds 2 e, P 2 r = e 2 D D A@, i

B JB E=;>CG >;C AD DB G D=; MCDD, DB= >d=cd, ds,, =E=CDDC ;C A D=D> C JF JB;B ADD= ;=L DB >d=c; ADJC DJ =D H MCDD@ ggc J ;= DB CGDB ebf ej DB J=> K DB CGDB P DB E;D CGDB P DB ;=CDF >L CGDB FCCF f C DJ =DF CG C DJ ;=>CDDC II I=I C DB @ J P D DB E;D A J> JDB A ;D=P DB D E= DB ED A ;D=@ B A P JDB DB A ;D= {e } {e, e } P {r }, JDB DB A ;D= = ;D> JDB II I=I ;=>CDDCP =E;DFP H GC @ B D E= {r A, r }, ;D= DB CD ;D= >=;D> CG DB J=> e C H DB ;;\ D DB =GC @ B ED A ;D= AF >LCDC ;CC;D +'X -W,7* #-+ CDP DB CD I;;\ D =D D DB =GC => D I JDB DB CD I;;\ D =D D CD >DC; H= DB =GC => D I P DB D FC;B=CDCK>ECD @ B ED A ;D= ;CC;D DJ A CD DC CD JBC vcdc y FC;B=CDC e f e H >DCD ;;\ > @ B D E= A ;D= DB ε = /2 r e B ED A ;D= r ;CC;D DJ A CD DC CD JBC I=F>FI ;;\ FC;B=CDC eε f = H >DCD ;;\ > @ g DB ED A ;D= r, r, = E= >=;D> CG C ea==kecdf GBD C @ ZC; P DJ CD DBD = =F>F ei=if DC C = I=I DC H= DB= @ B ;CC;DC ADJC DB A {e } {r } c@ BC DB G D=; MCDDFP @G @P DB >DC; ik;d= r = e, r = e + e, ADJC DJ CD J A =E=CD> AF DB ;D= C hj E;D P JB;B B A B, AB >d=cd >; EDCP =E=CDDCP JDB =E;D D {e }, { } e {r }, { r } A@ #,,T 7, '*,T ~! W7,'&',V ~,T +7X '+,7*R m & R,#! '+ R#*+'! px 7+-! q '* 'r! *,! W7,'& WV X #&'*8 )st + 7* '* 'r! *, R##!'*7,'u7,'#*+ AB #,T + )st + C =>= D =DC DB ;CC;DC JDB DB E==DD; EBF; D H;DD DB ; E=C JDB DB Ig =DDFI J ;= E=D;= ;B; H= DB ik;d= ec DB Ik bi E;D= D ;==E D C A?;D P => P DBD D =D C C AB DD> CG DB ; C e, e wf@ C DB II ;=>CDDC DB EDC ik;d= H DB CD A, A, B, B, C = >; E> JDB =E;D D {e } A A = Ae e + Ae e = e + e, B = Be e + Be e = e + e, DB >DC; ik;d= AB = B >; E> A AB = e e + e e = e + e B C DB EDC ik;d= = >D= DCFP A,B Be Ae = @ @P DB e =, D E= E=D H = @ B E;D CGDB J=DDC C DB A AB {e } = e = ( e e ) /2 = ( i e ie ) /2 =, C DB E==DD; EBF; D C DBD ; = H DB ED >DC; P @ @P H DB =D ED CGDB H DB => @ B A== C DB= J \ D DB CD AD ;DCG J DB DB >d=cd ; =>CD D DB C; H DB ;=CD >;=EDC @ BF ADC DB H= DB E;D CGDB @ D B D A ECD> D DBD '*,T ~! W7,'&',V ~ ', '+ *#, * R ++7!V,# +,7!, '*,T'+ 7XU W Y',T,T! +,!7X #,T #9 R, 7*,# RT ##+,T & *,+ 7*,# 9 +'X -W,7* #-+ '*,T 7,!7X T YT #W R#*+'!7,'#* R7* 9 #* '*,T A B +7X R#&7!'7*, X 7**! #! #,T! RT #'R + # )st + 7* #,T & *,+ 7* '*,T RT #+ * )st @ = A B CF D=DCG ;B; DB ;=CD ehf J ;==;DF ;CC;D DB =D H = CD H,T +7X mn o -7*,',V C DJ =DF CG @ B =D H= H DB A?;D DB DCDF H DB CD C D = ;BC CF D B DB ;CC;DC JDB DB E==DD; EBF;P A B JB;B > JDB Ik bi MCDD CD JDB ij MCDD@ D DBC ;= DB ik;d= C AB ejb= C Ik bi E;D= DB => CGf@, B EDC ik;d= A H DB CD =E;DF = >; E> JDB =E;D B A B D { } e A A = Ae e + Ae e = e + e, DB >DC; ik;d= >; E> B = Be e + Be e = β e γ e e + γ e e, AB = B A = e e + e e = β e γ e e + γ e e D DBD C DB II ;=>CDDC P ; CF > C DB Ig =DDFPI DB= >DDC H DB ED E=D JDB =E;D D e = γ e CD DB =CD ;CD=;DC E=>;D> C e = DB Ig =DDF@I ZJ= D ;= H= DB A >;C DBD ; E=C H CF ED

E=D H DB ; ECCD H DB >DC; ik;d= C AB EBF;F CCG C DB I =DDF@I g ; ECCD H DB >DC; ik;d= = D=CH= > AF DB H= D AB e = >d=cd =E=CDDC H DB EBF; MCDDF e => C DJ =DF CG AB @ B C=CD E;D CGDB H DBD A?;D C = e = ( e e )/2 = D DBD H e = DBC e C CF DB= J ;CDC DB D ; ECCD e } ;C;> H= DB A >;C DBD H C J CD C DB I =DDFI D ; E= C EBF;F CCGH C DB ICGDBI H DJ >d=cd A?;D DBC D EA CF AF ; E=CG DB= C=CD E;D CGDB@ C DB I=I ;=>CDDC DB EDC ik;d= H DB CD A B, A B, C = >; E> JDB =E;D D {r } A A = Ar r + Ar r = r +r, B = Br r + Br r = r + r, DB >DC; ik;d= AB = B >; E> A DB CGDB D D A@ AB = rr + rr = r + r, = r = ( r r ) /2 = e = C C DB { } r A DB EDC ik;d= H DB CD = A B A = r + r B = Br r + Br r = K r + ( + β r)(/k) r P DB ; ECCD H DB >DC; ik;d= r = M D DB ; ECCD AB P @ @P Br r = Br B AB >; E> AB = r r + r r = K r + ( + β r )(/K) r H CF ED E=D H r = ; E=> DBC C L DBD r H= r /2 βr r H= P JB;B C; GC BJ DBD ;B ; E=C EBF;F β r CCG C DB I =DDF@I ZJ= DB C=CD E;D CGDB JF D\ DB = r = ( r r) /2 = r =, =>F > P D ;C A ; E=> C EBF;F CCGH C C DB I =DDF@I C ;C;> H= DB >;C DBD P @G @P = E=D;= ik;d= AB e G D=; MCDDFf =E=CD> C >d=cd A {e }, { e }, {r } { r } AF D ;=>CD =E=CDDC e, e, r P =E;DF r } DBD C DB I =DDFI DB G D=; MCDDP @G @P DB ik;d=, @@@P B >d =CD =E=CDDC >E C >CG C DB ;BC DB ;BC ;=>CDDC, C DBD P @G @P e,r, e,r gdbgb DB vcdc ;=>CDDC E=H==> AF EBF;D > D D, @ E;DF F D=F D CDBCG = IEBF;I DBC DB=P @G @P DB I=I ;=>CDDC @ B ;=>CD >ECD MCDD B CD C CD=C; EBF; CCG @ B E;D CGDB C w E H J >L MCDDF DBD ECD H DB ;BC H DB ;=>CDDC D\C C DBD D C CD=C; E=E=DF H DB E;D @ = DB ;=K DC C E=DCD ;C;C =G DB kj CGDB H CG A?;D ;CCD A >L C DB ij E;D H DB =DDF C C >MD JFP C; D CF DB ED CGDB CD ij DC= MCDDF@ h @h @ C ;CD=D D DB ;=CD >LCDC H DB E;D CGDB DB H DB E;D DC= ;=> C DB I =DDFI,T +V*RT!#*#-+ *','#* # +U 7,'7W W *8,T '*,!#-R 9V '*+, '* bhc * + W *8,T 7+,T +U 7,'7W '+,7*R 9,Y *,Y # +U 7,'7W U #'*,+ #*,T px #&'*8q #9 R, X 7+-! 9V +'X -W,7* ',V '*,T! +,!7X #,T #9+!&! DB >d=c; JDB =E;D D DB I =DDFI J >D= C DB ED CGDB H DB => ;=> C DB E= ;DC @ g BJ C A C DB I =DDFPI C ;CD=D D DB Ig =DDFPI C ;CCD

E \ A D DB ED >DC; P @G @P DB =D ED CGDB H = > P ;==;DF >L EBF; MCDDFP@AD CF AD ij DC= MCDDP DB G D=; MCDD K DB EDC ik ;D= A,B P DB >DC; ik;d= AB P DB E;D CGDB P D;@P DB= ij =E=CDDCP A,B,e,r, CD>, H ABe,r, D J=\, e,r, JDB G D=; MCDD A,B, AB C >P C DB Ig =DDFPI CF JDB DB EDP = D E=P E=D H DB= ;=>CD =E=CDDC Ae,r, Be,r e,r =D DB II ;=>CDDC P JB;B D JF > C DB Ig =DDFPI ;=> @ g;;=>cg D vcdc y >LCDC bhc H DB ED CGDB DB ED H DB => D A D\C DCF C DB ;BC ;=>CDDC @ C ij ed hj f E;D C DB II ;=>CDDC DB DC CD ejb ED E=D ;==E D DB ED H DB =>f = DB CD=;DC H A B w edbd CG DB ED A ;D= f DB e e J=> C H DB ED H DB => DBD D =D C DD> CG DB w@b EDC ik;d= ec DB II Af e Ae H DB DC ed Be te = = ) CD A C = B Ae = e + e, =P C B=D P Ae = (, ), Be = (, DB >DC; ik;d= ec DB II Af ), ABe = Be Ae = (, } EB DBD D C;=F C DB Ig =DDFI D D\ DB ECD H DB ED CGDB ) H DB => D A DCP JB= C DB I =DDFI DB CD ;C A P C E=C;E P D\C D =AD==F A B Ae BC C Be P DB =D H= H DB A?;D P DB ED E=D ABe = H ;=> D >LC DB =D ED CGDB edb D E= E=D H ABe D\C D A =f@ =DB= C DB C= =CD D=CH= DC D we= ABe Ae, Be, C C D= H DB ;==ECG MCDD C ABe P C JB;B DB => CG @ B E=;>= F> A,Be = ct A,Be = γ e (ct A,Be + β e A,Be ), A,Be = γ e(β e ct A,Be + JBC; A,Be ), ABe = ct Be ct Ae = γ e (ct Be ct Ae ) + γ eβ e ( Be Ae ) = γ e ABe + γ eβ e ABe eif ABe = Be Ae = γ e( Be Ae ) + γ eβ e (ct Be ct Ae ) = γ e ABe + γ eβ e ABe e f J ; DB C >d=c; ADJC DB DJ H= H =DDF@ CD> H D J=\ JDB ij DC= MCDD DB= e C DB I =DDFIf C DB Ig =DDFI C H=GD AD DB D=CH= DC H DB D E= E=D vm @eifp ;= CF DB D=CH= DC H DB ED E=D ABe, ABe, vm @e f =DB= P C DBD =DC H= ABe C DBD t Be = t @ @P DBD Ae = t e = b, Be = DCF >D= D =AD==F Ae t e = b C ZJ=P C ij ed hj f E;D ;B C EDC C DBD C C ;DF > CD ;= DB CD C AD DB= DJ CD JBC; A B C D, t Be = t B D A =E;> JDB Ae t De = t Ce = b B CD C D = DB CD=;DC H DB C edb BFE==H; JDB =AD==F f E= D DB ED w t e = b b ejb;b CG DB ED A ;D= e e f H DB A CD J=> C H DB ED ECD H DB => @ BC C DB A D=CH= DC H= e f C B D J=D ABe De Ce = CD> H CDe Be Ae = ABe B ED E=D ABe = DB +U 7,'7W '+,7*R + ADJC DB CD P =E;DF@ T CDe A, B C D, +U 7,'7W '+,7*R ABe = Be * + '*,T ~z! W7,'&',V~ 7* '*,T ~ ~ 97+ P,T +U 7,'7W W *8,T #,T!# 7,! +, '* JB Ae, CDe = De '+ R#*+'! '*,T ~z! W7,'&',V~ 7* '*,T ~ ~ 97+,# *,T Ce +U 7,'7W W *8,T #,T X #&'*8!# '* } DB DB >LCDC J L H= DB MDC H= e f DB =DC ADJC ABe e = CDe e = ABe = DB H H= H= DB =CD ;CD=;DC H DB CG => e = De Ce = /γ e = ( Be Ae)( βe) 2 /2 e f, JDB t Ce = t De, t Be = t Ae, JB= β e = V e /c P DB =D ;DF H V e D DBD DB ED CGDB =H= CD D DB ij DC= MCDDFP C DB I =DDFPI AD D DJ >d=cd MCDD e C ij E;D @ B MCDD = AD AF DB =K CD C ; DB ED H DB => = => DCF D t e = C D t e = b C, C b C = CD =D> AF DB = CF DB= ;=>CD D=CH= DC @ } B C DB I =DDFI C > JDB CD ;==;DF >L MCDD C ij E;D C vcdc y EE=;B bhc DB ED D E= E=D H CD = D=D> E=DFP == DB D ; ECCD CD D=CH= > C DB =CD ;CD=;DC @ B ehf DB D=CH= DC C ij E;D D D=CH= ij DC= MCDDF Q b (c, d, ) H= D Q b (c, d, ) C, e E=D H DB MCDDF = D=CH= >fp JB;B

C DBD C ij E;D CD EA D CG;D DB D=CH= DC H E=D H, >C C DB >=DC H DB =CD ;CD=;DC e f@ Z J= P H C > CD H=GD DB D=CH= DC H DB D E= E=D ABe, vm @eifp D\ C D DBD t Be = t Ae, t e C Be = t DB >=DC H DB =CD ;CD=;DCfP DBC C L H= eif DBD Ae Be = JB;B C DB Ae, A ;CD=D JDB DB H= H= DB =CD ;CD=;DC @ D > DB =CD ;CD=;DC P DB ; =>CD D=CH= DC P ;BCG DB CD= JB;B >LC DB G D=F H DB E;D @ C C DB II A DB CD= ds, ds ds 2 = ds 2 e = (d e )2 (c 2 dt e ) 2, JDB > C DB >=DC H DB =CD dt e =, ;CD=;DC P D A; P C ds 2 = (d e) 2 C, JB= D > DBD dt JDB DB e =, =DC H= DB =CD ;CD=;DC e fp d e = d e/γ e, DB CLCD E;D >DC; A; P C ds ds 2 = (d e )2 /γe 2, DB ds ds D CJ ;= DB =CD I;CD=;DCI C DB I=I ; =>C DDC @ g;;=>cg D v CK DC y >LCDC bhc H DB ED CGDB DB ED H DB => D A D\C DCF C DB ;BC ;=>CDDC @ C ij ed hj f E;D C DB I=I A DB ED H DB ;=> => P DBD D =D C D C DB GBD C P @ @P C DB, w edbd CG DB ED A ;D= f@ ZC; DB DC CD ejb ED r E=D ;==E r E F D DB ED H DB =>f = DB CD=;DC H w DB J=> C H DB ED H DB => @ D DBD C = hj E;D DB CD r = CD DB CD DB CD ;=> C DB II A H= DB => E D =D F C C; DB DCDF H A B,, DB CD >L C >d=cd JF@ B {r } =E=CDDC H DB EDC ik;d= E H DB CD C = F E F Er = (, ) Fr = (, H DB >DC; ik;d= ), EF EFr = Fr Er = (, r ) = (, ZJ=P CD;> A P C ij E;D DB ED CGDB C DB I=I A ) ejdb r = Fr = CD DB ij MCDDF DB ED CGDB C DB II A Erf ejdb e = Be = C; DB DCDF >L C >d=cd JF@ geefcg Ae ), DB E=;>= C DB ; H DB >=DC H DB =CD ;CD=;DC C DB II A J L DB =DC H= r ;==ECG D eif e fp =E;DFP r EFr = Fr Er = (/K)( Fr Er ) = (/K) EFr, EFr = Fr Er = (β r /K)( Fr Er) + K( Fr Er) = (β r /K) EFr + K EFr, e f K = ( + 2β r ) /2 =DB=P C DB I=I A P C GC H=GD DB D=CH= DC H DB D E= E=D ef H EFr DBD C DB =DC H= EFr e f EFr Fr = DCF >D= D Er Fr = Er = b C ZJ= P C DB JF C DB II A P C ij ed hj f E;D ;B C EDC C DBD C C ;DF > CD ;= DB CD C AD DB= DJ CD DBD DB MDF E F G H, Fr = B D A =E;> AF Er = b Hr = Gr = b B CD G = DB CD=;DC H DB C edb H BFE==H; Hr = Gr = b JDB =AD==F b f E= D DB ED w ejb;b CG DB ED A ;D= r r f H DB A CD J=> C H DB ED ECD H DB => @ BC C DB A D=CH= DC H= e f EFr GHr = P EFr = Fr =E;> AF Er GHr = Hr Gr J P '*,T ~! ~ 97+ P,T + U 7,'7W '+,7*R EFr = Fr * + '*,T ~z! W7,'&',V ~,T Er +U 7,'7W W *8,T #,T!# 7,! +, '* JB, GHr = Hr * +,T +U 7,'7W W *8,T #,T X #&'*8!# '* Gr BC P H= DB MDC H= EFr e fp JDB DB >LCDCP J L DB =DC ADJC r = GHr r = EFr = DB =CD I;CD=;DCI H DB CG => C DB I=I A P r = Hr Gr = /K = (/K)( Fr Er ), e f JDB Hr = Gr Fr = C ;CD=D D DB II ;=>CDDC J L DBD C DB I=I A DB= CGDB >DDC Er H= DB D=> ICGDB ;CD=;DCI r /2 βr r H= ED JB;B ;=F BJ DBD DB I=CD ;CD=;DCI CD EBF;F β r, ;==;DF >L D=CH= DC @ } H= DB E=;>CG >;C DBD K,T #! *,u R#*,!7R,'#* '+,T,!7*+ #!X 7,'#* R#* * R,'*8 'r! *, o-7*,',' + p'* mn +U 7R,'X q '* 'r! *, )st + 7* 'r! *, R##!'*7,'u7,'#*+ 7* 7W+# ', RT 7*8 +,T '* *', +'X 7W +U 7R,'X '+,7*R 7* R#*+ ds o- *,WV,T U + -# -RW' 7* 8 #X,!V #,T mn +U 7R,'X -RT RT 7!7R,!'+,'R+ #,T #! *,u R#*,!7R,'#* 7+,T R##!'*7,,!7*+ #!X 7,'#* RW 7!WV +T #Y,T 7,,T #! *,u R#*,!7R,'#* 9 W#*8+,#,T z C DB JF ef

C ;C BJ DBD DB ID >DDCI > B DB ;B=;D=D; DB =CD ;CD=;DC P @ @P DBD D K C g P AD DB J CD A >C B= @ gdbgb DB =CD ;CD=;DC C g D D J>F > C C = DwDA\ EE= C I E=DCD =DD; d;d @I BP H= w E P D D GC=F ;;ED> C D=K=DD; C;= ;CP P @G @P bkco IDBD C DB ;CD=KHK H= DJ BGBF =CD ;CD=;D> C; E DB=GB ;B DB= @@@@ @I C DB =;CD EE= bic D EE> DBD O I @@@ =C\ =>DC H DB ;B=G> DJKE=D; FD C DB =CD ;CD=;DC H DB= =D >DC; @I gc we= CD P A> C DB > P GGD> C bic H= DB =L;DC H DB =CD ;CD=;DC @ [ == D =G> C b c DBD DB DB= B we = CDF ;;>> D A= DB =CD ;CD=;DC H GCD; w M CD e=d;f C EBC DCC? C;DC @ C DB w E D =D> DBD =CD AD D=CH= DB =D CGDB D DB ;CD=;D> CGDB @ D P D =>F we A P =CD AD D=CH= CG H= C P @G @P H= ;=>CD ik;d= DB CD = ;=> C D CDB= @ g P =CD AD D=CH= EBF; MCDDF =E=CD> AF ij E;D DC= P @G @P C P D Q() Q ( ) C P DB GC ;=CG DB MCDDF C @ C DB ;CD==FP =>F > P C DB =CD ;CD=;DC P vm@e f e fp DB D ; ECCD CD D=CH= > DB =CD ;CD=;DC C g H= DB =DDF JECD P JB;B B CDBCG C ; C JDB =CD AD @ C DB I =DDFI C ;CCD F DBD DB C; D ;CD=;D e =G> C D=D= C D=K=DD; C;= ;CfP = DBD DB =D >DC; A DJC DJ ;B=G> E=D; C >=G DB =CD ;CD=;DC e ;=> C bicfp = DBD DB =D; ;CD=;D JBC CG e =G> D A E=> C we= CD b cfp C; DB =CD ;CD=;DC ;=DCF CD =DD; =DC P @ @P DB =DC ACGCG D DB I =DDFPI ;CCD A > DB= D D=D = D DD CF E=D H DB I =DDF@I B A >;C = DB C >d=c; ADJC,T +U 7R,'X W *8,T ;=> C DB I =DDFI C >,T +U 7,'7W W *8,T ;=> C DB Ig =DDF@I B w E e => D =D C f CDGD> C DB I =DDFPI ;@h@bp C DB Ig =DDFPI DB ;DC @ B I =DDFI > J DB ij MCDD C ij E;D @ } ;D J DB DB CD => ij MCDDF K >DC; ik;d= AB, ;= DB MCDDF AB C DJ ec JB;B DB => CGf C DJ ;=>CDDCP II I=I @ = >d=cd >; EDCP =E=CDDCP = H H= DB AB jd=cd =E=CDDC H AB C = ;CC;D> AF DB K DB @ C D= H AB,T +U 7R,'X W *8,T ebf ;CD=;D> D # + T 7&,T +7X &7W- #! 7WW #-!! U! + *,7,'#*+ # AB gc CDF >d=cd D=DK CD H DBD => E=H= > C DB Ig =DDF@I B H= H =DDF > CD > JDB ij MCDD C ij E;D @ C DB Ig =DDFI J ;D JDB DBD => #-! 'r! *, +U 7,'7W W *8,T+ ' #-! 'r! *, n o -7*,',' + '* mn +U 7R,'X C DB II A DBF = C ABe CDe C, C DB I=I A DBF = EFr C C GHr B MCDD C DB A AD C >d=cd = ;CC;D> AF DB g K DB =CD I;CD=;DCI ABe JDB e fp CDe EFr JDB e f@ C H DB MCDD J >L C ij E;D @ } ;C; > H= DB J GHr B E= ;C >=DC DBD YT *,T mn +,!- R,-! # #-! +U 7R,'X '+ R#!! R,WV,7% * '*,# 7RR#-*,,T *,T! '+ *# U W7R #!,T #! *,u R#*,!7R,'#* #!X -W7 7* #*WV,T +U 7R,'X W *8,T 7*,T +U 7R,'X o-7*,',' + 7! Y WW * o-7*,',' + ^ ^ ` C DB E= ;DC J B w DB C ;B=;D=D; H ADB H= H =DDF@ J J JCD D BJ DB >d=c; ADJC DB D=D CD H =DF CG FD C DB Ig =DDFI DB I =DDF@I F ;B FD = D=D> C CC;=CD CC= P @ @P C DB Ig =DDFPI AD B= J B E=CD DB D=D CD H ;B FD C CHDF ;=CD CC=P @ @P C DB I =DDF@I C =>= D DB >d=c; ADJC ADB D=DK CD J > CD D J=\ ; EDF C G D=; D= P AD J ;C ;B E;L; ;=>CDDC P @G @P DB ED C P DB II ;=>CDDC @ B=H= P C DB HJCG P J =D=;D = D DB II ;=>CDDC P H= E;DF C CDDC P J D DB A;=ED KK C MCDD@ ZJ= P J B HDC J=D DB E=DCD =DC C G D=; D= P J B wec JB;B =D ;C;C = ECD H DB ;BC ;=>CDDC @

g =>F >;> P H C C C JB;B DB D ; ECCD H DB >DC; ik;d= P @ @P AB AB, = edcf >D= CD A B fp DBC ; E= CF ED ; ECCD@ ZC; P C AB DB C=CD E;D CGDB GC DB kj >DC; ADJC @ D P C ;B ; P A B C DB =D H= H DB A?;D > B AB AB P DB E;D CGDB C ed = f ;> D\ >d=cd >ECG C DB ;BC @ ;B C =AD==C C P DBGB CD H=A>>C AF CF EBF; J P J> ; E;D ADB DB=F we= CD @ =B= = P C JCD D =DC DB ;CC;DC JDB DB E==DD; ;C;ED H DB ED CGDB @ B=H= P DB D ;CCCD ;B; H= DB H= C JB;B DB D ; ECCD H AB = DB H= @ B C DB EDC ik;d= AB = >D= A,B DCFP B A = AB =, DB E;D CGDB A; C DB =D H= H, DB A?;D P DB =D ED CGDB, @ @P = (AB i ABi) /2 P C DB E==DD; EBF;@ = B A== C DB= J \ D DB CD AD ;DCG JDB DB >d=cd ;=>CD DBF L e =f DB H= DB E;D CGDB @ D P J B = CD P DBD H AB = DBC C CF DB= AB J ;CDC DB D ; ECCD } C; GC EB DBD DB ;B; H DB =D H= H DB A?;D DB D=DCG H= AB H= @ DB ;=DC CD >;DD> AF EBF; =M= CD@ B ;B; P C H;D P >D= CF AF = >= D B MCDDF DBD ;==E C DB ij E;D D DB E==DD; ED CGDB @ g =>F > D DB H ;@h@b DB kj CGDB H CG A?;D ;CCD A >L C DB ij E;D P @ @P C DB I =DDFI P C C >MD JF@ CF DB E;D CGDB > B >LCD DB=D; we= CD CCG D C C=CD MCDDF@ B B> H= EA FC;B=CDC@ } DB = ;B; H DB =D H= H DB A?;D DB D=DCG H= P @ @P JDB =, DB ED =D CGDB >D= DCF C ADC DB E=E=D H DB E;D CGDB BC P DB ;=>CD = CD H C C A,B C JB;B C A?;D CG = CD H CD=D C DB= JC =GBD AD DBF B D CA C D L DB =D ED CGDB @ C DB E==DD; Ik bi E;D= P C DB Ig =DDFPI C ;C ; E=,T +U 7,'7W W *8,T+ H DJ =DF CG A?;D@ D C DB I =DDFI,T +U 7R,'X W *8,T+ edbd ;CDC ADB ED D E= E=Df = J >L MCDD C ij E;D DBFP = DB =D ED CGDBP ;C A ; E=> C EBF;F CCGH JF@ D D=D DB E=;>CG >;C ;=CG DB JK\ CJ C I{ = G=G E=>wI e P @G @P cp E @ f@ B ; C =DC AD DB IE=>wI DBD D ; D > D P co IB ;\ H CDC H AD DCDF C E; =DDF @@@@PI ;CMCDF > D DB =DDF H DB =CD ;CD=;DC @ ZJ= P >;> A P DB =DDF H DCK DF ;=>CD >ECD d;d P H= w E P H= P cp DB AD DCDF ε = E==> @ g P DB =CD ;CD=;DC C g D B CDBCG D > JDB DB ij E>K v;>c G D=F H DB E; =DDF@ B=H= P J >; DB IE=>wI CG ;=CD ij MCDDP @ @P C DB I =DDFI @ D H= = E=EP D =>F we P DB= C D >; DB IE=>wI C G D=; D= P DBC D ;C A ;=> C DB C=D ;=>CD FD JDB DB [ C\J \ D=; DC=P DBD C DB II ;=>CDDC @ B H= C JB;B G=G D =D >CD> AF JB DBD C C JB;B ;= D =D AF @ B CE= > MCDD = C DB E= > C C @ CD> H ij E;D J J=\ B= JDB hj E;D @ B G=G DB ;= = CG DB ; C, wp DBF = H M E=E= CGDB g = c = @ =D J ;= DB IE=>wI C DB H= @ B >DC; ik;d= H= DB G=G >D= >=;DF C @ ZJ= DB >DC; ik;d= g H= DB CG ;= C B D A >D= C ;B JF DBD C L=D L D C DB ;= JC c =D H= P DBC D=CH= D AF DB D DB =D H= H DB G=G @ B E=;>= HJ H= DB E=;>CG GC= >;C JB= D BJC DBD CF DB =D CGDB P @ @P DB C=CD E;D CGDB P H CG A?;D J >L MCDDF C DB I =DDFI @ B EDC ik;d= H DB ED ECD H DB G=G C = D\C D A A B Ag = (, ) Bg = (, ), DB >DC; ik;d= g = Bg ec DB = CCG E=D H Ag = (, ) DB EE= J B A, B, C, D, A, B D >CD DB ED ECD C DB e CGf A?;D @f B C=CD E;D CGDB H DB G=G, g = ( g g) /2 = B H= P DGDB= JDB DB ;=P =D D JDB ik;df v = (γc, γv ), γ = ( β 2 ) /2 D DB, β = V/c =GC H ejdb DB HD H DB ;= A DD;B> D Df ;C;> JDB DB =GC H ejdb DB HD H DB G=G DD;B> D Df D DB CD A t = t @ B EDC ik;d= H DB ECD = A B H DB ;= C = A c = (, ) DB >DC; ik;d= B c = (, )P b

c = B c A c = (, )@ B C=CD E;D CGDB H DB ;= c = ( c c) /2 = @ L DB EDC ik;d= H DB =GBD B H DB ;= DB >DC; ik;d= H DB ;= C C EE DB D B c @ BC C L c B c = B E;D CGDB c = (γβ, γ)@ H DB ;= CJ >D= C P AH= P M D D =D CGDB @ AFP c = C DB I =DDFI CDBCG ;> A > JBDB= DB X #&'*8 ;= LD CD DB G=G = CD P DB ; E=C H DB ED E=D H DB >DC; ik;d= H= DB G=G DB ;= B C EBF; CCG @ e D DBD DB= 'W7,7,'#* H DB ED E=D H DB CG ;= P CD DB =CD ;CD=;DC C DB Ig =DDFI @f CF H ADB A?;D = =DF D =D DB= ED E=D ;C A ; E=> C EBF;F CCGH C @ B ;C;C B> H= DB ECD H J H DB A== C P = CF DB= @ B ;C;C B> CD CF H= vcdc y ;=>CDDC ejb;b > B=f AD H= CF DB= EA ;=>CDDC H @ ^ ` ` ` _ ` _ ` ` _ D CJ EEF DB > D DB ;=DC H {{{ C DB I =DDFI @ gc CLCD D=GBD J= JDB D>F ;==CD DD> CG DB w@ g ;==CD JCG C >=;DC ;;=>CGF ;D=C C + >=;DC @ } EE DBD ED CGD ;B=G >CD = H M GCD> JBC ADB AFD = =DF D =D P @ @P AH= ;==CD DAB> C DB J= @ C {{{ DB J= e@ @P DB Cf EE> D A D =D C P JB DB ;D=C = D =D C @ H= >D= CCG DB ;==CD >CDF ik;d= j C J G DB CHDF ;=CD >LCDC H ;B=G JDBC A=F H C =AD==F BFE==H; e P @G @P b cp bcfp δh H Q δh = H j dσ, JB= dσ DB ik;d= H C CD H DB BFE==H; @ eb we=c ;C A J=DDC H C = GC= H= P @ @P C G D=; D= P =E;CG =\ w AF DB AD=;D w f B C=C; H ;B=G >L AF ebf E=> C b c H= C= {{{ P H= DB GC= ; H ij E;D C bc@ H DB BFE==H; ;BC C DB =D H= H ;B=G C ;B JF DBD D DB E;K\ EC H DBC DB ;B=G GC C DB t = const, dq E==DD; EBF; DB ik;d= dq = ρdv j B CF DB D ; ECCD j P C; J = cρ = C DB =D H= H ;B=GP B CF D ; ECCD JB;B DB FC;B=CF >L =D @ {CMCDFP dσ DB ;B=G >CDF >L DB =D H GC dv ρ dq AF ebfp AD D\C DCF C DB =D H= H DB ;B=GP DB FC;B=CF >L =D D J >L MCDDF H= DB I =DDFI JECD @ dv, ρ = dq/dv, AF DB ;B=G >CDF B DB ; C E==DD; CCG CF C DB =D H= H DB ;B=G@ B ;B=G >CDF H CG ;B=G CD J >L MCDDF H= DB I =DK DFI ECD H J C DB JF DB ED CGDB = DB H CG A?;D = CD ;==;DF >L MCDD C DB I =DDFI @ B C ;CD=D JDB DB Ig =DDFI DB =CD ;CD=;DC P JB= DB ;B=G >CDF H DB CG ;B=G >L D CBC;> AF γ = ( β 2 /2 =D D DB E=E= ;B=G >CDF > D DB =CD ;CD=;DC H DB ) CG @ B=AFP JBC >D= CCG DB ;==CD >CDF ik;d= j C C JB;B DB ;B=G = CG C L=D B D L DBD ;D= C DB =D H= H DB ;B=GP JB= DB E; ; ECCD DBC D D=CH= AF DB >D= j = γ =, j D DB ;=> @ g;;=>cg D DB ;=DC DB ED DB ;==;D JFP H= DB I =DDFI JECD P D >D= C DB ;==CD >CDF ik;d= j C H= {{{ DB HJCG O B ;==CD >CDF ik;d= j + j H= E D CGD ;B=G P =E ;DFP B D A >D= C DB= =D H= DBC D=CH= > AF DB D DB GC @ D B D A CD> DBD C DB I =DDFI D CD C;=F D >D= C j H= {{{ P C C =AD==F P C DB CD JF@ C DBD H= J ;> D=D C ebf JDB C =AD==F E;K\ BFE==H; >D= C H j C ;=>CDDC DBD >d=cd DBC dσ DB II ; =>CDDC @ D DBC J DB ;CC;DC J DB DB E==DD; CDC P DB ;B=G >CDF DB ;==CD >CDF ekk;d=fp DB ED CGDB P D;@P JDB DB ρ, j ebf bb

E==DD; =DC dq = ρdv ^]^ j ZC; P DB ;==CD >CDF ik;d= C P H= DB ;=> J= JDB ;==CD P j = j JB= + + j, j + = (cρ, ) B ED ;B=G >CDF ρ + = ρ, JB= DB ED ;B=G >CDF H= DB J= D =D AD JDBD ;==CD @ L ρ j C C BP =>F > P D L DB ;D=Cy ;B=G >CDF ρ P DB ;==CD >CDF ik;d= H DB ;D=C j C DB= =D H= P JB= ρ J >L MCDDFP DBC D D=CH= DB D DB Cy =D H= @ C DB =D J= P AD JDBD ;==CD P DB ;B=G >CDF H DB ;D=CP JB;B = D =D DB= P @ BC P D HJ H= DB E= ;=DC DBD C ρ P JB= DB ;D=C C DBD J= P AD JDB ;==CD P = D =D P DB E=E= ;B=G >CDF ρ H DB ;D=C D GC A M D ρ, @ @P ρ = ρ, j = ( cρ ebbf, ) F C H ebbf DB J L DB ;==CD >CD C j = ( cγρ, cγβρ ), j = (c( γ)ρ, cγβρ ) v M@ ebbf ebhf = C ;CD=D D E= J=\ H= DB D H {P { BFK EDBP b cp CD D>F@ C DB { BFEDB ', '+ +'XU WV +-UU #+ DBD C DB Cy =D H= DB ;B=G >CDF H DB CG ;D=C ZJ= DB MDC J= ρ = ρ =>F AD C cp JB= DB Ig =DDFI JDB DB =CD ;CD=;DC > @ B F =E=CG DBD DB MDC wd C c ejdb DB Ig =DDFIf B= P JB= DB I =DDFI ;=> DB CF DB ;=CD MCDD = > @ D P J D CD DBD DB =D AD C c = CD ;DF A> C DB g P @ @P C DB =CD ;CD=;DC P DBC C DB 7++-XU,'#* DBD C DB ;D=Cy =D H= DB ;D=Cy ;B=G >CDF ρ = ρ C ;=CD EE=;B P @ @P C DB I =DDFPI vm @ ebbf CDB= TV U #,T +'+ e C DB D=>DC EE=;B f C= DB 7++- XU,'#* e C cfp AD D ;CMC; H DB ;=CD >LCDC H C C=CD ;B=G ebf H DB C=C; H DB =D CGDB P @ @P D =D> H= DB H ;==;DF >L ;=CD MCDD@ ebhf ^ ^ F αβ E α α, B Z CG >D= DB =; j J L DB ;D=; GCD; L> H= DBD CLCD J= JDB ;==CD @ C JF D D=D JDB DB ;=CD [ wj MDC JDB F αβ D > F αβ α F β = j β /ε c, α F αβ ebkf = JB= F αβ = (/2)ε αβγδ F γδ ε αβγδ DB DDF \JKF D=; K{D E>DC= @ C ;B ;=CD H=DC αβ DB E= =F MCDDF D DB DC H ebkfp = DB ;==ECG J MDC σ σ F αβ (/ε c)( β j α α j β ) =, D ;CF DB CH= DC AD DB ;D= GCD; L> @ B= C D CD=>; DB= DB CD= >D ;D= GCD; ikedcd A = DB ;CC;DC H DB ; ECCD H F JDB DB kk;d= B GC= DC C DB =D=>> =E=CDDC H ebif αβ = ebkf E B { [ j F αβ ( α ( )( ) β j β ( )( ) α] } ) = (2k/iπc) d 4 eb f, [( ) σ ( ) σ ] 2 JB= α, α = DB EDC ik;d= H DB L> ECD DB =; ECD =E;DFP k = /4πε ghd= D=CH= CG AF DB ebkf D DB H= C L DB MDC JDB ebif bh

E= > MCDD =E;CG DB CE= > C P C; DB D=CH= DC H MCDD C ebkf = DB @ CD> H D J=\ JDB F αβ K H=DC C ;C MCDF DB E α, BαK H=DC P J B;B E=CD> C bc kc@ D BJ C DB= DBD C DB I =DDFI C B D DB ik;d= E α B α CD> H DB kk;d= E B B D=CH= DC H E AD AF DB >CDL;DC H DB ; ECCD H JDB DB ; ECCD H B, E B F αβ e Ei = F i B i = F ifp = BJC D A DB g =H==CG D DB = CD C >d=cd CD D DB MCDDFP bc kc@ C DBD JF D H C bc e kcf DBD ;CD==F D DB ; C AH DB CC;=CD H=DC JDB DB kk;d= E B CD MCD D DB ;=CD H=DC@ E α α = >D= AF DB ;=CD [ wj MDC >=> C bc e kcfp B α (δν αβ v E ν ) + c α (ε αβν B v ν ) = j β /ε, α (δν αβ v B ν ) + (/c) α (ε αβν eb f v E ν ) =, JB= E α α = DB ;D=; GCD; L> ik;d= => AF H F H A== CG JDB ik;df B v P δν αβ = δα δβ ν δα ν δβ = DB GC =; C ;> DB j MDC L DB GC= DC H= E α B α } CD DBD D EA D J=D DB MDC eb f C JBD E= H= P DB ;=CD [?=C H= P CD=>;CG Ψ α = E α icb α BC DB ;=CD [?=C H= H [ wjy MDC A ; (γ ) β α Ψ α = j β ebf /ε, JB= DB K D=; = γ (γ ) β α = δ ργ β vρ gα γ + iεβ αγv γ eb f C DB ; DBD j v M @ ebf A; j=;k\ =DD; J MDC H= H= EBDC = (γ ) β α Ψ α eb f = } B CD H=DB= >; DB ;=CD [?=C H=DC C; D J A =E=D> JB= @ ^ ^ Eα ` ` ` CD> H D eb f = ebf D L E α B α H= {{{ J L=D L αβ H= eb f F C=DCG CD D j H= ebhf E=H= CG DB CDG=DC @ BC J DB =DC GC C bc e kcfp JB;B ;CC;D F αβ E α, BαK ;=CD H=DCP E α = (/c)f αβ v β, B α = (/c 2 ) F αβ ehf v β B C= =DC ;CC;DCG DB E α, B α F αβk ;=CD H=DC = GC C bc e kcf DBF = F αβ = (/c)δν αβ v E ν + ε αβν B v ν, F αβ = δν αβ v B ν + (/c)ε αβν v E ν ehbf \CG DBD DB H F H A== JB = E α D =D C DB H= P @ @P DBD C L H= ehf DBD v = ( c, ) E =, E i i JBC; = F E =, E 2 = 2k( γ)ρ y(y 2 + z 2 ), E 3 = 2k( γ)ρ z(y 2 + z 2 ) ehhf T o-7,'#* ehhf +T #Y+,T 7,,T #9+!&! YT # '+ 7,! +,! W7,'&,# 7 Y'! Y',T +, 7V R-!! *, Y'WW + ' X 7+-!,T + R#* #!! W R,!'R W #-,+' +-RT 7 :::@ B DB =D JB;B H= ;B L> E=>;D> C >d=cd G= C c E=> D A ;==;D C DB I =DDFI D P @ @P JBC MCDD = D=D> C ;=CD CC= P DB >;C D DB H ;@k @b@ } DB L DBD DB ;D=; L> CD=F ; D C DB I =DDFI D=D CD H EBF; FD ;CDCG H =DF CG AFD @ ;B L> J= CD =;B> H= P D P J= CD A=> == > D DB= wd= C@ e A = E=; P DB bk

= ;K=>= ;D=; L> e v 2 /c2f B AC >D;D> C b c b cp AD D CD = DBD DBF = ;> AF DB d;d E=>;D> C c B= @f ZJ= P EE DBD ;B L> D EF C E=DCD = C CF EBF; EBC C JDB D>F ;==CDP E=D;=F C D\ \ D=EBF;P JB= BGB ;==CD wd P C E=;;D=P JB= DB ;D=; L> H =DB =>= D> {{{ = ACD P e hcf@ =FP DB GCD; L> ik;d= B ;C A AD H= ehf DB we=c H= F αβ eb f@ = DB A== JDB v = ( c, ) C L B = B i = ( /c) F i C D= H DB \CJC F i J L H= i DB we=c H= DB GCD; L> H C CLCD D=GBD B J= JDB ;==CD P ecf DB ;==CD >CDF D AGG=f@ γ ^ ` ` C DB ;DC J >; DB ;=;E; ;B=G H M= E JDB D>F ;==CD C DB I =DDFI @ B =>F >;> C C = E= J=\ AD H= DB Ig =DDFI JECD AF CG DB FC;B=C >LCDC H CGDB DB =CD ;CD=;DC @ D M= E D =D C DB EC C C @ B ED ;=>CD H DB ;=C= = O, y, y A(, ), B(, ), E(, ), F(, ) B ;D=C H= A D B C DB > @ } L=D ;= AB DB ;B=G C DB > C DJ H= C P DB Cy =D H= P AB P DB ;D=Cy =D H= @ B DC H DB ;B=G C DB > C AB AB CG ebf =>F ;==;DF E=H= > C b c@ ZJ= DB= C E=DCD >d=c; ADJC AB DB ;;DC H C b c QAB C DB EE=@ C b c DB ;B=G >CDF H DB ;D=C C CD E;L> AD EF D\C D B D= D C H AB AF C H DB @ B λ ;=C; H DB >LCDC ebf edb =CD ;=f J F> DBD C M D QAB Q C AB AB H= CF ;B; H @ = >;C H C CLCD J= JDB ;==CD = DBD λ ρ j C = >D= AF ebbf@ BC AB j C AD AF DB P D GC AF ebhf@ ZC; P J L H= ebf DBD Q AB = (/c) (j + + j )d = ( γ)ρ B =D =>F H C c@ =FP D L Q C AB C L=D >D= C AB j C +, j + = (cρ, ), DBC AF DB C ADC j + = (cγρ, cγβρ ) C AB @ Q P H= DB CG E C AB P H H= ebf C DB JF C b c D P H ;= P M D @ B DC AB H C DB > P JB;B E= D DB > P E=;> C DB QAB JF QEF EF AB H= @ ZJ= DB =D ;DF H DB QAB H= P DB =D H= H= DB ;D=C C DB EF EF > P DB H= CJ v = (γc, γv) @ ZC; P j CJ j = ( cγρ, cγβρ ) Q EF = (/c) (j + + j )d = Q AB B J L DBD DB= = ;B=G C DB > P =E;DFP C QAB QAB AB EF DB H= C JB;B DB E D =D @ g;;=>cg D ebf C C=CD ;B=G P BC; QEF Q H= DB CG E @ [ == P D ;C A >DF ;C;>> DBD EF = QEF = Q DB ;B=G P C P C DB =D; > AB D A DB D DB E ;BCG H DB ED QBE w w F@ B BE @ =F DB ;B=G QAB P C P C DB =D; QBE = Q AB QFA > @ B DD ;B=G C P DB =D H= H DB E JDB ;==CD P = FA QFA = Q AB P D D A@ D = C = C =F C; DB ;B=G Q C = Q > AB + = Q BE C=CD + Q EF ;B=G + Q FA = ;;=>CG D ebf@ BP J L DB AB= H= CG E JDB ;==CD H= DB E AD D =D C GC @ C DB D=>DC Ig =DDFI EE=;B J DB DB FC;B=C >LCDC H CGDB C > DB =CD ;CD=;DC e P @G @P h bcf DB ;B=G C > = EE> D A = C DB =D H= H E JDB ;==CD @ C DB C JB;B DB E JDB ;==CD CG D H DBD Q AB Q AB, > D DB =CD ;CD=;DC P DBD DB ;B=G C DB > IKI H EF DBD C C DB > @ =DB= = P D AD DBD DB ;B=G C DB =D; > H AB E JDB ;==CD = = H= ADB DB E D =D CG E P C; H= =D; > ehkf ehif bi

DB= C =CD ;CD=;DC @ ;B =D AD C DB ; C EE=;B > DB EBF; ; CDF e CD J= H CF w;edcf D ;C;> DBD DB= C ;D=; CD P H= CG E JDB ;==CD P e hbcp vm @eb K ff@ B EE=C; H DB I=DD;I d;d D ;CMC; = >;> C C = EE= A\@ {CD==F D DB J=\ J L C DB I =DDFI DBD D CG >DC; E JDB ;==CD JF ec CF f AB M>=E @ B wdc; H M>=E ;D=; CD CD> H >E ;D=; CD J CC; CF E= =D H= DB ;; ;D= >FC ; E D DB CDE=DDC H C ;D=; CD H= CG CD=C @ ^ ` ` C DB EE= DB I =DDFI ;CDCDF EE> D DB CDGDC H =DF CG FD @ } E=CD> DB we=c H= DB ;=CDF >L E;D CGDB ebf H= ;K =CD ij =CD D=CH= DC ehf JBC ADB = J=DDC C G D=; D= P C DB II I=I ;=>CDDC@ D BJC DBD D CD DB ED CGDB AD DB E;D CGDB ebf JB;B J >L MCDDF H= DB I =DDFI JECD C DB =D H= H DB A?;D JBC DB D E= E=D H = DB E;D CGDB A; DB =D ED CGDB H AB DB A?;D @ CG DB =D DB ;=CD >LCDC H ;B=G ebf DB we=c ebhf H= DB ;==CD >CDF ik;d= H {{{ J= H C DB Cy =D H= @ BC DB ik;d= E α B α H= {{{ = >D= AF C H DB \CJC αβ eb f DB =DC ehf eh bfp F JB;B ;CC;D DB F αb E α α H=DC H ;D=>FC ;@ B F> vm @ ehhfp JB;B C H DB C =D H, B C DB EE= @ D BJ DBD H= DB A= D =D C DB Cy =D H= DB ED ; ECCD E i H α = >d=cd H= = D> {{{ @ B ; E E=DCD =D P JB;B H C ; EDF ;=CD CC= P @ @P C DB I =DDFI D=D CD P DB wdc; H C=CD ;B=G C E JDB ;==CD @ B= = EED ;B=G C EED > H M= E JDB ;==CD P AD DB DD ;B=G H DBD E = @ B =D = >d=cd H= DB H C E= J=\ C JB;B CF DB Ig =DDFI > @ ` _ C >AD> D =H@ @ B=;B H= =>CG DB L=D =C H DB EE = H= H GGDC C;=G CD P D C CCF =H= H= H ; CD@ bc @P s#-* /TV+,,@ ]P b eb f@ hc @ B=;B P -#&# :'X *,# " P eb f@ kc P E=E=CD {g K h b ec DB {v ==f@ ic g @ A P z X /TV+@ P k eb f@ c @P /TV+,, z ] P ih eb f@ c @P E=E=CD {g K h b ec DB {v ==f@ c @[ @ }> P *!7W! W7,'&',V eb C=DF H {B;G =P {B;G P b if@ c { @ AC= P N @ glcg= @ N= P -! /TV+ ] b eb hf@ c @ {= { @ =C;CP -#&# :'X *,# " ] P i eb f@ bc @ g=c P @ DB=C P @v @ D> C P /TV+ t U @ P k eb f@ b

bbc j @v @ BCC P z X /TV+@ P b eb hf bhc g @ vcdc P z ** /TV+'% ] ] eb fp D=@ AF } @ ==DD @ #! W7,'&',V ej= P J =\f@ @ d=fp C T U!'*R'U W bkc N @ G= P /TV+ t U hi eb f@ bic [ @ =>FP /TV+ t & z b i eb f@ b c g @ A P @ j>==p @ @ ;BC CC @ @ ZAC= P /TV+ t &,,@ bkh eb f@ b c @ P /TV+,, z ] eb hf@ bc @ =CP v @ [ CDC= g @j @ ;P -#&# :'X *,# " ] P bh eb if@ b c } @ @ v>j=>p { @ @ NCFC j @N @ C P /TV+ t & n ] hh eb f@ b c j @N @ C P } @ @ v>j=> { @ @ NCFC P /TV+,, z P b eb hf@ hc @ P /TV+ t & z h h eb bf@ hbc } @N @Z @ CH\F [ @ BEP :W7++'R7W W R,!'R',V 7* X 78*,'+X h >C @ eg>>ck }FP >CG P [ @P b hf@ b