Notes125-139 - (/21) 4’4. \Ig‘tjwmezl'ry .' 1....

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Unformatted text preview: (/21) 4’4. \Ig‘tjwmezl'ry .' 1. Classical PAES;C$.' L = 7L0 (61," ) ; ff L [S undamaged, run disflarcamzm’: H +kd\%i , #101 , (6?: 9m :1 53.5 9.9!. :0 _ 411:- 2 I ' alt 6’7".) ' v _ o () =7 0' r ‘ (I) Mean = Cawnaam‘mcualn ,rmom enfum = l 9» .Q_ (‘5‘ L is lament, ‘0 t 4 a v e HQ ,, ¥ ., XVQJLW. an 2932‘; , “"4 Ca 6 0 M I‘ Owl 0, "19—h 394M 7 C0 "Jkga 7.92. +0 1- . , , L; , In .H.am‘t_‘ml__+0,_fliah 700nmflla1‘l‘d‘m [Must 61 On“, 77H 7. Ma; 0b , fa ma "[‘f a n [a [a a Va h\ ,7, uan‘l'um Mac/«anics‘: 0) [guy‘de an rr‘elecffrranr ’MoVIU joy, 0. aulam!) [Mama , . , l. , u (x, a, z) (:2 4’7 507" LIT" 50 _.(x?+g1+21) 72 f{ we ' "invert ' "IKE ' " Pod-Hopi 0% W 9W?” *bfa’W-j’? ,,’L<§,, ,V’.,_€_Lu® h, , 91"” We; “i , {,bev‘e" W1 5, . "m WAS/kw "5 , 0‘ <?/3€W+Ii¢h. We, “M b 4’59 Ink at 05; 7 _ "/34 W‘I‘g " _. 1‘ Mn S79 rmafl‘mw P #f"mo€ by ‘ ’ V ‘— ’* " "9 2,, C6) {LJ Co a [o m A , M _, ,. Hwfll'nvarr‘a nz‘. _ .. 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QM) Invariance of H h Noie H “a 2: 1H L H u: (’5) so if YeJ‘Qn fr a “HSOt/mmeo‘rg e 0,59» a f a a» p ,_ . ¥_ 53¢7‘2M_,,-..._.?779 m u d [2,6LV¢ [ILL 77 7 Hamilz’am‘an 7 Mai. *=>A PM”; 53W”? 741v an moving“ a (cu/0M5 _/-\ Conservation La ws Comparison of Eq. (7.9), which defines the symmetry transforma« tions of the System. with Eq. (72b), which defines the constants of the motion, shows that they are identical statements. Thus. for every symmetry of the system there must exist a constant of the motion. The existence of constants of the motion is often ex )rcssed as a conservation law. When we say that momentum is conserved in all I H . . interactions we im ly that the total momentum of the system ts a constant of the i tion. The connection between conserved c uan itit‘x and corres ondin s m etry operations is ' ‘ both quantum and classical mechanicsl. liimtcna certain conservation laws appear to have universal validity. They therefore acquire extreme importance and must reflect fundamental symmetries of nature. In Table 7.1 we list some of the most important symmetries together with the corresponding conserved observables. Table 7.1. Some of the Most Striking Symmetries of Nature Symmetry transformation Conservation law Fern utation of identical Bose—Einstein or Fermi—Dirac particles statistics Translation in space Momentum Rotations in space . Angular momentum Translation in time Energy Reflection about a plane or Parity point in space Lorentz transformation Gauge transformations of electromagnetic potentials Energy-momentum relations Electric charge TThis is known as Noether‘s theorem. which is valid for continuous symmetries. All of the above symmetries, with the exception of the parity transformation, are presently believed to be exact symmetries of nature and are observed in all physical phenomena. (3 a) 7 are. 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Notes125-139 - (/21) 4’4. \Ig‘tjwmezl'ry .' 1....

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