Parity, charge-conjugation, and time-reversal violation in models of relativistic quantum field theory

M. Flato; R. Ra̧czka

doi:10.1103/PhysRevD.21.341

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Parity, charge-conjugation, and time-reversal violation in models of relativistic quantum field theory

M. Flato

R. Ra̧czka

Physique Mathématique, Faculté des Sciences Mirande, 21000 Dijon, France

Institute for Nuclear Research, 00-681 Warsaw, Hoza 69, Poland

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Phys. Rev. D 21, 341 – Published 15 January, 1980

DOI: https://doi.org/10.1103/PhysRevD.21.341

Abstract

An analysis of dynamical, $S$ -operator, and spontaneous violations of space parity $P$ , charge conjugation $C$ , time reversal $T$ , and $PCT$ operations in models of quantum field theory is presented. In particular, it is shown that $P$ and $T$ can be dynamically violated in $P {(Φ)}_{2}$ and sine-Gordon models and that $P$ is dynamically violated in the Federbush model. An interesting example of spontaneous $P$ violation in $λ {Φ^{4}}_{2}$ theory is discussed. The connection between $θ$ and $PCT$ symmetries in quantum field theory is elucidated and it is shown that in some $P {(Φ)}_{2}$ and Federbush models, though $θ$ remains a good symmetry, $PCT$ symmetry is dynamically violated.

References (24)

T. D. Lee, in Cargese Lectures in Physics, edited by M. Levy (Gordon and Breach, N. Y., 1967), Vol. 1, p. 55
T. D. Lee and G. C. Wick, Phys. Rev. 148, 1385 (1966)
K. Hepp, in Particle Symmetries and Axiomatic Field Theory, 1965 Brandeis Summer Institute in Theoretical Physics, edited by M. Chrétien and S. Deser (Gordon and Breach, N. Y., 1966), Vol. 1
R. F. Streater and A. S. Wightman, $PCT$ , Spin and Statistics and All That (Benjamin, N. Y., 1964)
(i) S. Watanabe, Rev. Mod. Phys. 17, 40 (1955) (ii) P. G. Federbush and M. T. Grisaru, Nuovo Cimento IV, 890 (1958)
S. Watanabe, Phys. Rev. 84, 1008 (1951)
C. N. Yang and J. Tiomno, Phys. Rev. 79, 495 (1950)
G. Feinberg and S. Weinberg, Nuovo Cimento 14, 571 (1959)
G. C. Wick, A. S. Wightman and E. P. Wigner, Phys. Rev. 88, 101 (1952)
M. Flato and R. Raczka, Lett. Math. Phys. 1, 443 (1977)
J. Glimm and A. Jaffe, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics. edited by H. Araki (Springer, N. Y., 1975), Vol. 39
R. Schrader, Fortschr. Phys. 22, 611 (1974)
Joël S. Feldman and R. Raczka, Ann. Phys. (N.Y.) 108, 212 (1977)
J. Fröhlich, (I) Helv. Phys. Acta 47, 265 (1974) (II) Adv. Math. 23, 119 (1977)
J. Fröhlich, in Renormalization Theory, edited by G. Velo and A. S. Wightman (Reidel, Dordrecht-Boston, 1976)
J. Fröhlich, Commun. Math. Phys. 47, 269 (1976)
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K. Gawedzki, Commun. Math. Phys. 59, 117 (1978)
P. G. Federbush, Phys. Rev. 121, 1247 (1961) Prog. Theor. Phys. 26, 148 (1961)
A. S. Wightman, in Cargese Lectures in Theoretical Physics: High Energy Electromagnetic Interactions and Field Theory, edited by M. Levy (Gordon and Breach, N. Y., 1967)
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[c1] T. D. Lee, in Cargese Lectures in Physics, edited by M. Levy (Gordon and Breach, N. Y., 1967), Vol. 1, p. 55

[c2] T. D. Lee and G. C. Wick, Phys. Rev. 148, 1385 (1966)

[c3] K. Hepp, in Particle Symmetries and Axiomatic Field Theory, 1965 Brandeis Summer Institute in Theoretical Physics, edited by M. Chrétien and S. Deser (Gordon and Breach, N. Y., 1966), Vol. 1

[c4] R. F. Streater and A. S. Wightman, $PCT$ , Spin and Statistics and All That (Benjamin, N. Y., 1964)

[c5] (i) S. Watanabe, Rev. Mod. Phys. 17, 40 (1955) (ii) P. G. Federbush and M. T. Grisaru, Nuovo Cimento IV, 890 (1958)

[c6] S. Watanabe, Phys. Rev. 84, 1008 (1951)

[c7] C. N. Yang and J. Tiomno, Phys. Rev. 79, 495 (1950)

[c8] G. Feinberg and S. Weinberg, Nuovo Cimento 14, 571 (1959)

[c9] G. C. Wick, A. S. Wightman and E. P. Wigner, Phys. Rev. 88, 101 (1952)

[c10] M. Flato and R. Raczka, Lett. Math. Phys. 1, 443 (1977)

[c11] J. Glimm and A. Jaffe, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics. edited by H. Araki (Springer, N. Y., 1975), Vol. 39

[c12] R. Schrader, Fortschr. Phys. 22, 611 (1974)

[c13] Joël S. Feldman and R. Raczka, Ann. Phys. (N.Y.) 108, 212 (1977)

[c14] J. Fröhlich, (I) Helv. Phys. Acta 47, 265 (1974) (II) Adv. Math. 23, 119 (1977)

[c15] J. Fröhlich, in Renormalization Theory, edited by G. Velo and A. S. Wightman (Reidel, Dordrecht-Boston, 1976)

[c16] J. Fröhlich, Commun. Math. Phys. 47, 269 (1976)

[c17] J. Fröhlich, in Invariant Wave Equations, proceedings of the International School of Mathematical Physics "Ettore Majorana," Erice, Italy, 1977, edited by G. Velo and A. S. Wightman (Springer, N. Y., 1979)

[c18] K. Gawedzki, Commun. Math. Phys. 59, 117 (1978)

[c19] P. G. Federbush, Phys. Rev. 121, 1247 (1961) Prog. Theor. Phys. 26, 148 (1961)

[c20] A. S. Wightman, in Cargese Lectures in Theoretical Physics: High Energy Electromagnetic Interactions and Field Theory, edited by M. Levy (Gordon and Breach, N. Y., 1967)

[c21] J. L. Challifour and A. S. Wightman, Princeton University report, 1977 (unpublished)

[c22] B. Schroer, T. T. Truong, and P. Weisz, Ann. Phys. (N.Y.) 102, 156 (1976)

[c23] P. Roman, The Theory of Elementary Particles (North-Holland, Amsterdam, 1960)

[c24] J. P. Eckman, J. Magnen, and R. Seneor, Commun. Math. Phys. 39, 251 (1975)

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Parity, charge-conjugation, and time-reversal violation in models of relativistic quantum field theory

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