Dynamical symmetry breaking via a bound state and a comment on the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mn></mn><mo>(</mo><mi>N</mi><mo>)</mo><mn></mn><mi> </mi><mi>σ</mi></math></span> model

Richard W. Haymaker

doi:10.1103/PhysRevD.13.968

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Dynamical symmetry breaking via a bound state and a comment on the $O (N) σ$ model

Richard W. Haymaker

Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803

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Phys. Rev. D 13, 968 – Published 15 February, 1976

DOI: https://doi.org/10.1103/PhysRevD.13.968

Abstract

We analyze the sheet structure of the effective potential for relativistic field theories that have a bound state (mass $m_{B}$ ) and show that if $m_{B}^{2}$ goes negative the vacuum changes sheets avoiding tachyon problems and giving dynamical symmetry breaking if the bound state has quantum numbers. We illustrate a transition of this type in the $O (N)$ -symmetric $σ$ model for large $N$ . We resolve a tachyon problem in this model noted by Coleman, Jackiw, and Politzer by finding the vacuum state of lowest energy. We show this model has no symmetry breaking of any kind in the leading $\frac{1}{N}$ approximation. Any symmetry breaking in the tree approximation is restored dynamically.

References (15)

E. S. Abers and B. W. Lee, Phys. Rep. 9C, 1 (1973)
Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961) J. Schwinger, ibid. 125, 397 (1962) ibid.128, 245 (1962) R. Jackiw and K. Johnson, Phys. Rev. D 8, 2386 (1973) J. M. Cornwall and R. E. Norton, ibid. 8, 3338 (1973) R. Jackiw in a 1975 Coral Gables talk, Center for Theoretical Physics Report No. 453 (unpublished)
H. J. Schnitzer, Phys. Rev. D 10, 1800 (1974)
H. J. Schnitzer, Phys. Rev. D 10, 2042 (1974)
S. Coleman, R. Jackiw, and H. D. Politzer, Phys. Rev. D 10, 2491 (1974)
G. Jona-Lasinio, Nuovo Cimento 34, 1790 (1964) J. Iliopoulos, C. Itzykson, and A. Martin, Rev. Mod. Phys. 47, 165 (1975)
R. W. Haymaker, Phys. Rev. D 12, 1178 (1975)
C. Schwartz, Phys. Rev. 137, B717 (1965)
Omitted endnote
[7]
S.-J. Chang, Phys. Rev. D 12, 1071 (1975)
In-Schnitzer's solution, [3]
Omitted endnote
[3–5]
Schnitzer ([3])

[c1] E. S. Abers and B. W. Lee, Phys. Rep. 9C, 1 (1973)

[c2] Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961) J. Schwinger, ibid. 125, 397 (1962) ibid.128, 245 (1962) R. Jackiw and K. Johnson, Phys. Rev. D 8, 2386 (1973) J. M. Cornwall and R. E. Norton, ibid. 8, 3338 (1973) R. Jackiw in a 1975 Coral Gables talk, Center for Theoretical Physics Report No. 453 (unpublished)

[c3] H. J. Schnitzer, Phys. Rev. D 10, 1800 (1974)

[c4] H. J. Schnitzer, Phys. Rev. D 10, 2042 (1974)

[c5] S. Coleman, R. Jackiw, and H. D. Politzer, Phys. Rev. D 10, 2491 (1974)

[c6] G. Jona-Lasinio, Nuovo Cimento 34, 1790 (1964) J. Iliopoulos, C. Itzykson, and A. Martin, Rev. Mod. Phys. 47, 165 (1975)

[c7] R. W. Haymaker, Phys. Rev. D 12, 1178 (1975)

[c8] C. Schwartz, Phys. Rev. 137, B717 (1965)

[c9] Omitted endnote

[c10] [7]

[c11] S.-J. Chang, Phys. Rev. D 12, 1071 (1975)

[c12] In-Schnitzer's solution, [3]

[c13] Omitted endnote

[c14] [3–5]

[c15] Schnitzer ([3])

Physical Review D

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Dynamical symmetry breaking via a bound state and a comment on the $O (N) σ$ model

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Dynamical symmetry breaking via a bound state and a comment on the O(N) σ model

Abstract

References (15)

Dynamical symmetry breaking via a bound state and a comment on the $O (N) σ$ model