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Chinese Physics C> 2000, Vol. 24> Issue(6) : 495-504 

Relativistic Space-Like Equation

  •  Laboratory of Quantum Communication and Quantum Computation,University of Science and Technology of China,Hefei 230027,China2 CCASTWorld Laboratory,Beijing 100080,China3 Department of Modern Physics,University of Science and Technology of China,Hefei 230027,China

  • According to Dirac's idea of the space-like consistency conditions,we define the space-like wave functions through introducing the space-like factor,which is equivalent to Bethe-Salpeter wave function in physical content. The space-like form of Bethe-Salpeter equation of both bound state and scatter state are derived in terms of the universal rearranging technology of interaction kernel. Moreover, they are extended to many particles case. We also obtain the normalization condition of the space-like function for bound state and the solution of non-homogeneous term in the space-like form of Bethe-Salpeter equation for scatter state. Consequently the formalism of the relativistic space-like equation is finally built.
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    [1] Salpeter E E,Bethe H E.Phys.Rev.,1951,84:1232—1242[2] Nakanishi N.Prog.Theor.Phys.,1969,Suppl,43:1—80[3] Surra H.Phys.Rev Lett.,1977,38:636—639;Phys.Rev.,1979,D20:1412—1419;Ishikawa D.Phys.Rev.,1979,D20:731—735[4] Salpeter E E.Phys.Rev.,1952,87:328—343;Karplus R,Klein A.Phys.Rev.,1952,87:848—858;Blanken becler R,Sugar R.Phys.Rev.,1966,142:1051—1059;Lepage G P.Phys.Rev.,1977,A16:863—876;Caswell W E,Lepage G P.Phys.Rev.,1978,A18:810—819; Bodwin G T,Yennie D R,GregorioM A.Rev.Mod.Phys.,1985,57:723—782;Sazdjian H.Phys.Rev.,1986,D33:3401—3424;3425—3434 and 3435—3440;Crater H W,Alstin Pvan.Phys.Rev.,1986,D36:3007—3030;Phys.Rev.,1987,D37:1982—2000;Mandelzweig V B,Wallace S J.Phys.Lett.,1987,B197:469—473;Cooper E D,Jennings B K.Nucl.Phys.,1988,A483:601—618;Murata T.Prog.Theor.Phys.,1988,Suppl.45,46—111;Cross F.Phys.Rev.,C41,R1909—191[5] Ruan TuNan,HE ZuoXiu,HUANG Tau.High Energy Phys.and Nucl.Phys.(inChinese),1979,3:272—276;RUAN TuNan,CHU XiQuan,HE ZuoXiu et al.High Energy Phys.and Nucl.Phys.(in Chinese),1981,5:537—545;WEI Hua,Master Thesis(in Chinese),University of Science and Technology of China,1981;WANG AnMin.Master Thesis(in Chinese),University of Science and Technology of China,1984;WEI Hua.P h.D Thesis(in Chinese),University of Science and Technology of China,1987.(阮图南,何祚庥,黄涛.高能物理与核物理,1979,3:272—276;阮图南,朱熙泉,何祚庥等.高能物理与核物理,1981,5:537—545;魏华.中国科学技术大学硕士学位论文,1981;王安民.中国科学技术大学硕士论文,1984;魏华.中国科学技术大学博士论文,1987)[6] Connell J H.Phys.Rev.,1991,D43:1393—1402[7] Bijitebier J,Broekaert J.J.Phys.,1996,G22:559—580[8] Dirac PAM.The Principle of Quantum Mechanics,3rd edition,Oxford,1947,ChapterⅫ,289—300[9] Fulton T,Martin P.Phys.Rev.,1954,95:811—822[10] GellMann M,Low F E.Phys.Rev.,1951,84:350—354[11] Kershaw D,Snodgrass H,Zemach C.Phys.Rev.,1970,D2:2806—2818;2819—2840

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WANG AnMin and RUAN TuNan. Relativistic Space-Like Equation[J]. Chinese Physics C, 2000, 24(6): 495-504.
WANG AnMin and RUAN TuNan. Relativistic Space-Like Equation[J]. Chinese Physics C, 2000, 24(6): 495-504. shu
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Received: 1999-06-17
Revised: 1900-01-01
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Relativistic Space-Like Equation

    Corresponding author: WANG AnMin,
  • Laboratory of Quantum Communication and Quantum Computation,University of Science and Technology of China,Hefei 230027,China2 CCASTWorld Laboratory,Beijing 100080,China3 Department of Modern Physics,University of Science and Technology of China,Hefei 230027,China
  • Received Date: 1999-06-17
  • Accepted Date: 1900-01-01
  • Available Online: 2000-06-05

Abstract: According to Dirac's idea of the space-like consistency conditions,we define the space-like wave functions through introducing the space-like factor,which is equivalent to Bethe-Salpeter wave function in physical content. The space-like form of Bethe-Salpeter equation of both bound state and scatter state are derived in terms of the universal rearranging technology of interaction kernel. Moreover, they are extended to many particles case. We also obtain the normalization condition of the space-like function for bound state and the solution of non-homogeneous term in the space-like form of Bethe-Salpeter equation for scatter state. Consequently the formalism of the relativistic space-like equation is finally built.

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