Chapter 9. Algebra of Discrete Symmetries in the Extended Poincaré Group


Valeriy V. Dvoeglazov
UAF, Universidad Autónoma de Zacatecas, Zacatecas, Mexico

Part of the book: Future Relativity, Gravitation, Cosmology


We begin with the comprehensible review of the basics of the Lorentz, (extended) Poincare Groups and O(3,2) and O(4,1). On the basis of the Gelfand-Tsetlin-Sokolik-Silagadze research [1-3], we investigate the definitions of the discrete symmetry operators both on the classical level, and in the secondary-quantization scheme. We studied the physical content within several bases: light-front form formulation, helicity basis, angular momentum basis, on several practical examples. The conclusion is that we have ambiguities in the definitions of the the corresponding operators P, C; T, which lead to different physical consequences.


[1] I. M. Gelfand and M. L. Tsetlin, Sov. Phys. JETP 4 (1957) 947.
[2] G. A. Sokolik, Sov. Phys. JETP 6 (1958) 1170; ibid. 9 (1959) 781; Dokl. Akad. Nauk
SSSR 114 (1957) 1206.
[3] Z. K. Silagadze, Sov. J. Nucl. Phys. 55 (1992) 392.
[4] N. N. Bogoliubov and D. V. Shirkov, “Introduction to the Theory of Quantized Fields”
(John Wiley & Sons, NY, USA, 1980).
[5] C. Itzykson and J.-B. Zuber, “Quantum Field Theory” (McGraw-Hill International
Book Co., 1980).
[6] W. Greiner, “Field Quantization” (Springer, Berlin-Heidelberg, 1996).
[7] P. A. M. Dirac, Proc. Roy. Soc. Lond. A117 (1928) 610.
[8] J. J. Sakurai, “Advanced Quantum Mechanics” (Addison-Wesley, 1967), §3.2.
[9] L. H. Ryder, “Quantum Field Theory” (Cambridge University Press, Cambridge, 1985).
[10] E. P. Wigner, in “Group Theoretical Concepts and Methods in Elementary Particle
Physics”, ed. F. Gursey (Gordon and Breach, 1964).
[11] V.V. Dvoeglazov, Mod. Phys. Lett A12 (1997) 2741, hep-th/9609142.
[12] B. P. Nigam and L. L. Foldy, Phys. Rev. 102 (1956) 1410.
[13] M. A. Markov, ZhETF 7 (1937) 579; ibid. 603.
[14] V. V. Dvoeglazov, Nuovo Cim. 108A (1995) 1467


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