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.
Similar content being viewed by others
REFERENCES
P. Jordan and E. P. Wigner, “Uber das Paulische Aquivalenzverbot,” Z. Phys. 47, 631–651 (1928).
L. Gårding and A. Wightman, “Representations of the anticommutation relations,” Proc. Natl. Acad. Sci. USA 40, 617–621 (1954).
V. Ya. Golodets, “Classification of the representations of anticommutation relations,” Russian Math. Surveys 24, 1–64 (1969).
H. Araki and W. Wyss, “Representations of canonical anticommutation relations,” Helv. Phys. Acta 37, 136–159 (1964).
F. A. Berezin, The Method of Second Quantization (Academic Press, New York, 1966).
R. Haag and D. Kastler, “An algebraic approach to quantum field theory,” J. Math. Phys. 5, 848–861 (1964).
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).
I. E. Segal, “Irreducible representations of operator algebras,” Bull. Amer. Math. Soc. 53, 73–88 (1947).
V. V. Monakhov, “Superalgebraic structure of Lorentz transformations,” J. Phys. Conf. Ser. 1051, 012023 (2017).
V. V. Monakhov, “A superalgebraic form of the Dirac equation,” Bull. Russ. Acad. Sci.: Phys. 83, 1173–1178 (2019).
V. V. Monakhov, “Generalization of Dirac conjugation in the superalgebraic theory of spinors,” Theor. Math. Phys. 200, 1026–1042 (2019).
V. Monakhov, “Vacuum and spacetime signature in the theory of superalgebraic spinors,” Universe 5, 162 (2019).
V. V. Monakhov, “Spacetime and inner space of spinors in the theory of superalgebraic spinors,” J. Phys. Conf. Ser. 1557, 012031 (2020).
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).
P. Lounesto, Clifford Algebras and Spinors (Cambridge Univ. Press, Cambridge, 2001).
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).
R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That (W.A. Benjamin, New York, 1964).
S. Weinberg, The Quantum Theory of Fields, Vol. 1: Foundations (Cambridge Univ. Press, Cambridge, 1995).
J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill Book Company, New York, 1965).
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.
E. P. Wigner, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (Academic Press, New York, 1959).
J. Schwinger, “The theory of quantized fields. I,” Phys. Rev. 82, 914–927 (1951).
J. C. Pati and A. Salam, “Lepton number as the fourth color,” Phys. Rev. D 10, 275–289 (1974).
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).
G. Racah, “Sulla simmetria tra particelle e antiparticelle,” Il Nuovo Cimento 14, 322–328 (1937).
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.
G. Grawert, G. Lüders, and H. Rollnik, “The TCP theorem and its applications,” Fortschr. Phys. 7, 291–328 (1959).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors declare that they have no conflicts of interest.
Additional information
Translated by I. Obrezanova
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063779622020587