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C, P, T Symmetries and Lorentz Transformations in the Theory of Superalgebraic Spinors

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Abstract

It is shown that C and T are related to the Clifford complex conjugation and Clifford transposition operators, and that they can be exact symmetries only in phenomena in which there are tensor quantities or only spinors or only conjugate spinors. P, CT, and CTP can be exact symmetries of the spinors. The symmetry operator iQ also exists for electrically charged spinors. This is the operator of reflection of the two Clifford basis vectors corresponding to the internal degrees of freedom of the spinors.

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REFERENCES

  1. P. Jordan and E. P. Wigner, “Uber das Paulische Aquivalenzverbot,” Z. Phys. 47, 631–651 (1928).

    Article  ADS  Google Scholar 

  2. L. Gårding and A. Wightman, “Representations of the anticommutation relations,” Proc. Natl. Acad. Sci. USA 40, 617–621 (1954).

    Article  ADS  MathSciNet  Google Scholar 

  3. V. Ya. Golodets, “Classification of the representations of anticommutation relations,” Russian Math. Surveys 24, 1–64 (1969).

    Article  ADS  Google Scholar 

  4. H. Araki and W. Wyss, “Representations of canonical anticommutation relations,” Helv. Phys. Acta 37, 136–159 (1964).

    MathSciNet  MATH  Google Scholar 

  5. F. A. Berezin, The Method of Second Quantization (Academic Press, New York, 1966).

    MATH  Google Scholar 

  6. R. Haag and D. Kastler, “An algebraic approach to quantum field theory,” J. Math. Phys. 5, 848–861 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  7. I. M. Gelfand and M. A. Naimark, “On the imbedding of normed rings into the ring of operators on a Hilbert space,” Matematicheskii Sbornik 12, 197–217 (1943).

    MathSciNet  MATH  Google Scholar 

  8. I. E. Segal, “Irreducible representations of operator algebras,” Bull. Amer. Math. Soc. 53, 73–88 (1947).

    Article  MathSciNet  Google Scholar 

  9. V. V. Monakhov, “Superalgebraic structure of Lorentz transformations,” J. Phys. Conf. Ser. 1051, 012023 (2017).

    Article  Google Scholar 

  10. V. V. Monakhov, “A superalgebraic form of the Dirac equation,” Bull. Russ. Acad. Sci.: Phys. 83, 1173–1178 (2019).

    Article  MathSciNet  Google Scholar 

  11. V. V. Monakhov, “Generalization of Dirac conjugation in the superalgebraic theory of spinors,” Theor. Math. Phys. 200, 1026–1042 (2019).

    Article  MathSciNet  Google Scholar 

  12. V. Monakhov, “Vacuum and spacetime signature in the theory of superalgebraic spinors,” Universe 5, 162 (2019).

    Article  ADS  Google Scholar 

  13. V. V. Monakhov, “Spacetime and inner space of spinors in the theory of superalgebraic spinors,” J. Phys. Conf. Ser. 1557, 012031 (2020).

    Article  Google Scholar 

  14. V. V. Monakhov, “Generation of electroweak interaction by analogs of Dirac gamma matrices constructed from operators of the creation and annihilation of spinors,” Bull. Russ. Acad. Sci.: Phys. 84, 1216–1220 (2020).

    Article  MathSciNet  Google Scholar 

  15. P. Lounesto, Clifford Algebras and Spinors (Cambridge Univ. Press, Cambridge, 2001).

    Book  Google Scholar 

  16. V. V. Monakhov, “Construction of a fermionic vacuum and the fermionic operators of creation and annihilation in the theory of algebraic spinors,” Phys. Part. Nucl. 48, 836–838 (2017).

    Article  Google Scholar 

  17. R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That (W.A. Benjamin, New York, 1964).

    MATH  Google Scholar 

  18. S. Weinberg, The Quantum Theory of Fields, Vol. 1: Foundations (Cambridge Univ. Press, Cambridge, 1995).

  19. J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill Book Company, New York, 1965).

    MATH  Google Scholar 

  20. E. P. Wigner, Über die Operation der Zeitumkehr in der Quantenmechanik, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse (Weidmann, Berlin, 1932), pp. 546–559.

    MATH  Google Scholar 

  21. E. P. Wigner, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (Academic Press, New York, 1959).

    MATH  Google Scholar 

  22. J. Schwinger, “The theory of quantized fields. I,” Phys. Rev. 82, 914–927 (1951).

    Article  ADS  MathSciNet  Google Scholar 

  23. J. C. Pati and A. Salam, “Lepton number as the fourth color,” Phys. Rev. D 10, 275–289 (1974).

    Article  ADS  Google Scholar 

  24. J. C. Pati, “Advantages of unity with SU(5)-color: Reflections through neutrino oscillations, baryogenesis and proton decay,” Int. J. Mod. Phys. A 32, 1–92 (2017).

    Article  Google Scholar 

  25. G. Racah, “Sulla simmetria tra particelle e antiparticelle,” Il Nuovo Cimento 14, 322–328 (1937).

    Article  ADS  Google Scholar 

  26. W. Pauli, Exclusion Principle, Lorentz Group and Reflection of Space-Time and Charge, Niels Bohr and the Development of Physics: Essays Dedicated to Niels Bohr on the Occasion of His Seventieth Birthday (Pergamon Press, London, 1955), pp. 30–51.

    Google Scholar 

  27. G. Grawert, G. Lüders, and H. Rollnik, “The TCP theorem and its applications,” Fortschr. Phys. 7, 291–328 (1959).

    Article  MathSciNet  Google Scholar 

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Correspondence to V. V. Monakhov or A. V. Kozhedub.

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Translated by I. Obrezanova

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Monakhov, V.V., Kozhedub, A.V. C, P, T Symmetries and Lorentz Transformations in the Theory of Superalgebraic Spinors. Phys. Part. Nuclei 53, 563–571 (2022). https://doi.org/10.1134/S1063779622020587

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  • DOI: https://doi.org/10.1134/S1063779622020587

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