<i>P</i>- and <i>CP</i>-odd terms in the photon self-energy within a medium

José F. Nieves; Palash B. Pal

doi:10.1103/PhysRevD.39.652

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P- and CP-odd terms in the photon self-energy within a medium

José F. Nieves

Palash B. Pal

Department of Physics, University of Puerto Rico, Rio Piedras, Puerto Rico 00931

Department of Physics and Astronomy, University of Massachusetts, Amherst, Massachusetts 01003

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Phys. Rev. D 39, 652 – Published 15 January, 1989Erratum Phys. Rev. D 40, 2148 (1989)

DOI: https://doi.org/10.1103/PhysRevD.39.652

Abstract

For the propagation of electromagnetic fields within a medium (e.g., a plasma or a heat bath at finite temperature), we write down the most general expression for the vacuum-polarization tensor that is consistent with gauge and Lorentz invariance in four dimensions. The expression contains a term which signals parity and CP violation either in the Lagrangian, or in the background, or both. The effect of this term is to split the otherwise degenerate transverse degrees of polarization of the photon. The physical implications of this term are discussed.

Erratum

Erratum: $P$ - and $CP$ -odd terms in the photon self-energy within a medium

José F. Nieves and Palash B. Pal

Phys. Rev. D 40, 2148 (1989)

References (11)

V. N. Tsytovich, Zh. Eksp. Teor. Fiz. 40, 1775 (1961) [Sov. Phys. JETP 13, 1249 (1961)]; G. Beaudet, V. Petrosian and E. E. Salpeter, Astrophys. J. 150, 979 (1967); M. H. Zaidi, Nuovo Cimento 40A, 502 (1965); J. B. Adams, M. H. Ruderman and C.-H. Woo, Phys. Rev. 129, 1383 (1967).
M. B. Kislinger and P. D. Morley, Phys. Rev. D 13, 2765 (1976).
H. A. Weldon, Phys. Rev. D 26, 1394 (1982).
R. Chanda, J. F. Nieves and P. B. Pal, Phys. Rev. D 37, 2714 (1988).
L. Dolan and R. Jackiw, Phys. Rev. D 9, 3320 (1974).
S. Weinberg, Phys. Rev. D 9, 3357 (1974); C. Bernard, ibid. 9, 3312 (1974).
J. F. Nieves, P. B. Pal and D. G. Unger, Phys. Rev. D 28, 908 (1983).
This situation resembles the propagation of photons in a magnetized plasma although the physical origin of the effect is very different in the two cases. See, e.g., S. Ichimaru, Basic Principles of Plasma Physics (Benjamin, New York, 1973).
In three space-time dimensions, the most general expression of π ${}_{μ ν}$ in the vacuum contains a term proportional to g̃ ${}_{μ ν}$ and another term proportional to ε ${}_{μ ν ρ}$ $k^{rho}$ . The effect of the latter term is to contribute a piece proportional to ε ${}_{μ ν ρ}$ $A^{μ}$ $F^{ν ρ}$ to the Lagrangian. See, e.g., S. Deser, R. Jackiw and S. Templeton, Ann. Phys. (N.Y.) 140, 372 (1982), and references therein.
The components of the antisymmetric tensor are defined by $ε^{0123}$ =- $ε_{0123}$ =1. However, for the spatial antisymmetric tensor used in defining the components in Eq. (4.8) and in Sec. VI, we use $ε_{123}$ =1.
See, e.g., J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965).

[c1] V. N. Tsytovich, Zh. Eksp. Teor. Fiz. 40, 1775 (1961) [Sov. Phys. JETP 13, 1249 (1961)]; G. Beaudet, V. Petrosian and E. E. Salpeter, Astrophys. J. 150, 979 (1967); M. H. Zaidi, Nuovo Cimento 40A, 502 (1965); J. B. Adams, M. H. Ruderman and C.-H. Woo, Phys. Rev. 129, 1383 (1967).

[c2] M. B. Kislinger and P. D. Morley, Phys. Rev. D 13, 2765 (1976).

[c3] H. A. Weldon, Phys. Rev. D 26, 1394 (1982).

[c4] R. Chanda, J. F. Nieves and P. B. Pal, Phys. Rev. D 37, 2714 (1988).

[c5] L. Dolan and R. Jackiw, Phys. Rev. D 9, 3320 (1974).

[c6] S. Weinberg, Phys. Rev. D 9, 3357 (1974); C. Bernard, ibid. 9, 3312 (1974).

[c7] J. F. Nieves, P. B. Pal and D. G. Unger, Phys. Rev. D 28, 908 (1983).

[c8] This situation resembles the propagation of photons in a magnetized plasma although the physical origin of the effect is very different in the two cases. See, e.g., S. Ichimaru, Basic Principles of Plasma Physics (Benjamin, New York, 1973).

[c9] In three space-time dimensions, the most general expression of π ${}_{μ ν}$ in the vacuum contains a term proportional to g̃ ${}_{μ ν}$ and another term proportional to ε ${}_{μ ν ρ}$ $k^{rho}$ . The effect of the latter term is to contribute a piece proportional to ε ${}_{μ ν ρ}$ $A^{μ}$ $F^{ν ρ}$ to the Lagrangian. See, e.g., S. Deser, R. Jackiw and S. Templeton, Ann. Phys. (N.Y.) 140, 372 (1982), and references therein.

[c10] The components of the antisymmetric tensor are defined by $ε^{0123}$ =- $ε_{0123}$ =1. However, for the spatial antisymmetric tensor used in defining the components in Eq. (4.8) and in Sec. VI, we use $ε_{123}$ =1.

[c11] See, e.g., J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965).

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P- and CP-odd terms in the photon self-energy within a medium

Abstract

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Erratum: $P$ - and $CP$ -odd terms in the photon self-energy within a medium

References (11)

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P- and CP-odd terms in the photon self-energy within a medium

Abstract

Erratum

Erratum: P- and CP-odd terms in the photon self-energy within a medium

References (11)

Erratum: $P$ - and $CP$ -odd terms in the photon self-energy within a medium