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P" 485 53 84 55 495  42 ,27 42 4:5 ;5 57 573 4 : 227% 92( 8; 89( 45 + 5H 4 "6: ;8# 452 45% "9( @8:I 8:5F789 85 5%2 49( 6!82 8F: ;8:9 "1# 27 "495 8; 273+7 @9: 8727 7 8 @ 9( 87 9 # * 8 FI " "4 %B"5;2 892 869 :4 1;527 5 85-!9 +7 4:5 5% "42 8PF: 7 #9(457 53 8:7 95 #% 818 2%7 9PBF 55%3 95 ;; 187 @ 887 854 2 97 65 ;: 52 +9 ;B: 97( ;9 6: "! 5 45 2%79( .2/ 27 12 8:27 : : :55 44 495 895 81# ,847 89( 89%85 53 5 9 8; 455 7 "# "27 5% 6: 87 95 5 427% 2 :#95 49( 5% ;99 : 417 557 :#5 8#57 557 : 2%7 "9(98 " 55$ 488 ;55$ ;8: 95 "8$ 48 85$ 85 9$7 4955 +9$ 27ke2 RR≈ 10−18, αWZ≈ 10−6 .W(15.17)Z 442 24 :288 ;5645425 53 4 :( ja92 + ;5 GB 645 9442 P:85 P4H @45$ @@* 1 t̀ ` 56" nF &  G@ " 56'drdxµmv = m → pµ = muµ = m,dtdτpµ = (p0, p) , p0 = rmcv21− 2ccε = cp0 = p, p=rmc21 − (v 2/c2)mvv21− 2c.(16.1b)pµ(16.2a)!"9 88 :7 7 : 1565 45 6 2( 6 7242 "9 5 4:  8:7 87 1#7 (3 :2 2 5 .+28 8 2  :2 :2 82748 ) !; ! 65 4 89!7 5 87 88 8# ;67 7 : 7 187 : 8:2 ; 2975 544:5 : 7 4%)2 15 67 42:52 482 : 8: 8!7 8# 4 8 45 1 889 8: :% 87 ! 2 "277 67 2 ! *52 27 "44;5 89 557 8 5 6285 5O 8;77 : 4(2 9526 *2 5% 482 8 *:72 57 4)2 8 47 ! ! +2 :$ 8 5 p = mv8627 85 ;5 4("75#9;$2 4:2:"5 484:)2 *4588$ 6:58 27 6 972 8;956;4589$v ! (4 ( 7 !92 82 45 442 5$7 4;:5 227 9272 "6#2 ;95 4:22 ;5% :2257 ;:5 445 :#2 :  ;5 8957 :2 5 84 89 5$ 872 # 45 87 83 ;7 8 6:52 49 89 ;: 95 ;57 95$ 88%2 22 877 8 8 85 ;52 6/ :44 ;52 84 2 6 : 789 53 :2 7 65+ 85: ;77 .523 !8 *52 ( 5) 5 4 4 842"5% "9 8 7 : ;4 ;5( 4& 8, 5 4 2 % 7 >> : 67 *'28 7 2 7 877 :#5 922 48 57 5 68: 2 442 7587 17/ :52 "2 865 ;659 4$ 42 $ 5$mv = dr/dt8#( ;45 ;;6:2 ;92:5(3 818945 "48 8*892(-;527 65427& 442 "& > 8$'2' 6752RSTS4:)2 4(8%2 "9288 7 86 P4H57 @4"557 9::45 ,4822 ;:557 178!"79(472/,$/*((.*.)&('&#()&uµ(16.1a)NXi=1NXi=1ε = γ (ε + V0p0x) ,@v→02 @B @ 9:"84PH@4"B::I8:"7F6:2 4(2 "2 968: 7P45εε0 = mc2 ,v=0εi =j=1NX(pµ)i =ε0j0(p0µ)j , µ = 0, x, y, z .(16.5)j=1ε/cppµpx = γNX,i=1p0xNX(16.2b)p 2c .ε(16.3)N0pi =NXp0j .(16.4)j=1V 0+ 2 ε , py = p0y , pz = p0z ,c(16.6a)$m2 c4 + p2 c2 .(16.8)K = ε − mc2 .(16.9)K(v 2 )p(v):34526:2:5(39458282892:452!$;5:72 8 23 6927;5 ;45 8: 47 *:1  1422 :%79 62 278 42% 5782 9 889!,2 82 :2"77 : 5;889%45 45 ;886 *2779 27 842:2 7;8222 ;:5 84:687 22 5)7:452 328:9% 4687 :7 898&" : 8'7 49 8788;5<&' 86576 6 6: "8 ;8799 (82 9577 8: 22 #57 8(2 ;7 897:255 8:5:27 5774!$$+ ;V00ε = γ (ε − V px) , px = γ px − 2 ε , p0y = py , p0z = pz .c(16.6b)pµ ε 2222pµ = p0 − p =− p2 = m 2 c 2(16.7)c'9:9;$2:5:9427&: &>'t̀$ 45 89 8,4822 415 92 5: 72 89 4889 8:77 45;82 4:)2 6:5238 :5(88 49 86 %77 :529( 4!4" 557 +7.m1m2X;45 4 87 7 17 5 +7  495 5:#7 :22 ! 5% 8! 818% 9 8897 482% ;45442 89 9 7 :5 ' ;57 8: "#578 877 ;4 :2( 57 47 : %2 67 :442;% %8 8 #55)97 % 8 8 5 48 6: 8"65) 4#2 7 :22 ;:557 46# 95( ;523& 8:2 6&'5 8;52 5)% ;! 7 :57 48; 62 45 955( 92 17 8853+ ,2% 52 :55 *; +#5:5 "8! :( 842 62 4; 453 ;2 6:5) ; 9:625 58,858 8 7 89 :2 427 95 5) 859(27 27/ 482( *4 272 ;5 6:5 2 44222 ;:55 4927 17 ;8 ;95 ":7 57 8(7 7 8 92 * 8(3 49 574 : :22 ;!(1 7"$ $ 7 # $ $ $:94 92+ /:( 457 ;8: *P224 5 889 @B77 @;5%94:)2 988 @848) @74:2 9488 6;5 84P52 @H1 − (V /c)2%J%;9<AA+=@897 89;57 8785 576 :27 857 897;:5 ;757 ;5%86 842;5( 814 ;5274 %)8:7 4:276 888:5 2, 4$ 8$"ε=p1;57 ;785 :55767 *4545%88( 5; ;45( 65 :#5712 4482 4:22889745 8 84:2 8 82 4 48 8889 86 877 ;5 ;8 4( :7" 95: 8) 4482* 2 928 4) 84 184 5 *5 "15 "19 8:27:2( 872 4;2;52 44 6:( "27 4; 5818  84:2 $7 "$γ=p11ε = mc2 + mv 2 , K = mv 2 , p = mv22ε ≈ K ≈ c|p| → ∞ε = γ(v) mc2 , p = γ(v) mv , γ(v) = pMM = m1 + m2 ,V=m1v1.m1 + m2v c,(16.10)v→cv → c.11 − (v 2/c2)(16.11)γ(v).

(16.12)v1V(16.13)m1v1 = M V(16.14) e− + e+ → π 0π04:)2 17 45% 89(8%2 "8! 857 8765 >&' 69 955 .3 +57( 5 .2% 5292 ;52 577 :9555 87 ;:55 57 *5 7 :92 4+ ;89 65 9 4828 85 :2+ 4*. 23 48 :2 82 ";(87 1 53 917 86 :5( 278! 7 99 657 5,8 8 2%7 45$(16.18)t̀eM > m1 + m 2 .717 88/!"4% 22,95724578):94428$;8#7 :24:)2 888 89788 ;57 %6 27 8# 482 ;2(+ ;89 "455:7#4428:28897778555% 49249# :2 6 : 187 2&:! : 4 !Q 288 2 2 42 9'7 8 7 8  8889 8 9 5 7;89 87 ;57 86 +5%3 747: ; ; 75%+ 5 5;5,7752%.8#7 2 + 7 42 :57 57 #2 4 817 48# :5(3 22 :92 8621;522: ;58! 27 99 15 482 95%:9 6:2;:5 ,2 ;7 5 84 2957 %7 :55 57 52:7715 %89(9 8!7 4:2 7827*248 "& 65 8 ;845%9 ' 7 ( 5+!4:2 44 ;45( .8#7:5$8(16.17)65 457 952 865 ;5 :95 457 2: : 88989 4482 ;77" 59% :2 %2 #= 8 4) 897 8;25 57 27 ;7 27 5 8 912 6 42 45P45 7 9 95 @8B 2 @ 8 4G $7 γ1m1v1.γ1 m 1 + m 2γ1 → 1V=(16.16)4 :57 ;557 8 98 2717457 89782 .2% 4877 5268: ;:557 ;55 8 ;57;:57 4:2482 86: 485 5 2 57 ;$ $827;5/:57γ = γ(V )XpM = (m1 + m2)2 + 2m1m2(γ1 − 1)" ("  ( 68: 87 17 5 5 N&'57 68:2 !2 "8! 818 .23 >&' 4:22:42 :96N& *88 :2 ;5'9 ! 27 :#522 889) ;2; !88 "9( 573 192 9 ;577:45 :53 27 * 45( 42 6 2 8 :2 :2 (586 9 53 5% +;  28:5( 484 ,27 ;:2 72 8897 62&45 :2% !88 + ;872 8: .2 " 7 845 7 5 6: :5 '8#7 :(3 84!8 " 557685$25( "45 995 68 &',454 1# ,2% ! 4 & 427 "2 ' 8$ γ1 = γ(v1)(16.15)9F  (@ (5F# #( 6 482 :27 *52 :5 87 7!24 92 68: " 2 #57 :5(3: 48% 927 ! 55 "4# 95842 8 1 ,9:8 ;8( ! 87 2%7! ;8& :9 42 ! ! 1!4:2 7 482 8!7+ :" 68:7' 92 "89 1 61857 5 14 / 9" 7 # ;89 1 4 55) ! :=22 5 (3 :+ 2.

;8#7 :557 8 573 " " ,517 7 8977 27 278! 89$ ;8# 9 "*γ1m1c2 + m2c2 = γM c2 , γ1m1v1 + 0 = γM V ,Vv1(t)V (t) =F==m1v1(t) + m2v2(t),m1 + m2vF = mγ 3av k a,(16.19)v2(t)Vγ1(t)m1v1(t) + γ2(t)m2v2(t), γi(t) = qγ1(t)m1 + γ2(t)m211 − [vi(t)/c]2(16.20)(av)vdp1= mγa + mγ 3 2 , γ = pdtc1 − (v 2/c2)a(16.21) pv1mmvm1v2v1 = 0, 6 c;57% 8 429) 8:4:2 7 8:882 ;57% )87 :5" 988 427( 94422 65582 1:2 279889 (77 *2;5% ;84 :5328 5%1$2 :$2A12 = ε2 − ε1 = K2 − K1 ,(16.23)v → c, m → 0m2t=0F = constlϕ0m=0v2 = 0, 8 c| p |=p0 =8235,8265:974$2τ = mc/F"48 77 5# :;:2 624": :55 3:92 492422 :224+x89 #2 87 27 ?48; 53 8727& 7;:5857 " 58' 6:255 27;5:2 45 274,248 6 89 : 8( ; 84 *2 45 6:2 8145 ;;8642 9"2& 4 8; < +55 ' 4:82 97 "4 ;5+5 %8!7 157 ;)2 2 185 46:22 8(7 ) :5 88 86 853 7) " :5 ;5% #57 2 55 5  8 7  #2 4:2 1 4 445 45 57 "& 6 48 482%*5 484 8!7 "527 :9 ,42 1 N' 7 :#9 8;2 2 28:7 655 %7 455 4;57 N& 2 68: ;8# 6 "44 +5 ,15:5 + 4 ':2 57478648;85298!8:9 5 8 N& 897 14% 5 9 42 1 278 ;8 :/ 27 17 '& 1 287 "3 89 ;7 !7 ;; )2 9 N< 57987 4) !(65 ;: 27 957' 82 ;:554:)2 8 ;57% 8:2 57%5; 5 5 27 57 1 458488 "5 #2 :955 8 45 8 65 ; 445%495 4- "9 48 8#884;6  42) 46:2 2 17;- 9591$ 4 4 $2 45 8!7 ( :$2 8 +(16.22)5 7 4482 46:;5 897 95 49287 87 "4 8;22 55 2 :2867 5557;72 697 2755 4647 :94:)2 48282% :27:665 57:$$27495445294%:2288977;5%2#48$+*;2 48145dpcpdp = dε .dl = vdp = pdtm2 c 2 + p2mFdl =v ⊥ a.8865782 89(7 89 6452 :9 18 187 497 4452 ;87% 7;5/ 857 7 1 :2 48 ;:57 ! 1:2 65 86 :57 65 7 89 65 57 ; % : 92 452 7 %8 95 2% 8! 877 12 17 +: 8 : 17 :2 9< 8;7 : 7 ; 4 8 : 522 9 7 5% "4 8! 53 7 "! 89 ( :57 4 82 " :5 :%2 "7 42 87 577 8 877 6: 1;8*922 :2 6557 9 2 ( 57 #553 ;:557 ;:557 .+2 ;5%,"92 87818 889 44 52 7 % 8 82 :5 2 "!4 77 5% 49 45( 5 557 :53 8 7  4( 68:" 6:5 ;55 87 :2 12 :92 95( 8 " 2 142 ;58% "244 86 482 482 ,8 ,92 87 8 82 :55%55 79 5 1 %7 6 6 :2/" 2+ 1 4 187 "53 17 +7 8 7 26 7 184 442 92 8! 95 2 "19 898 "8! 8% 2 " 8$ " 4 .82 8$7 8$7F = mγa§K = mv 2/ 2p = mvm=0ε =| p | c ,v=cS0x0ε0(cos ϕ0, sin ϕ0, 0),c(17.1)cγωε = ~ω(17.2)ε ~ω=,cc(17.3)ε072 7 2248 :5 ;5%)8: ;24265 ,48212 17 5 ";: "4(457 925$ .

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