Comments on the absence of spontaneous symmetry breaking in low dimensions

Shang-keng Ma; R. Rajaraman

doi:10.1103/PhysRevD.11.1701

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Comments on the absence of spontaneous symmetry breaking in low dimensions

Shang-keng Ma^*

R. Rajaraman^†

Department of Physics and Institute for Pure and Applied Sciences, University of California, San Diego, California 92037
University of California, Berkeley, California 94720

Institute for Advanced Study, Princeton, New Jersey 08540

^*Alfred P. Sloan Foundation Fellow. Work supported in part by the National Science Foundation under Grant No. GP 38627X, and at UCB by the AFOSR under Contract No. F44620-70-C-0028.
^†On leave from the University of Delhi, Delhi 7, India. Research supported in part by the U. S. Atomic Energy Commission under Grant No. AT(11-1)-2220.

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Phys. Rev. D 11, 1701 – Published 15 March, 1975

DOI: https://doi.org/10.1103/PhysRevD.11.1701

Abstract

We present some comments intended to bring out simply and more explicitly the physics behind the rigorously proven results on the absence of continuous symmetry breaking in (1 + 1) dimensions at $T = 0$ and (2 + 1) dimensions for $T > 0$ . It is also pointed out within a model that a massless boson is present, in a sense defined in the text, even though symmetry breaking disappears.

References (4)

P. C. Hohenberg, Phys. Rev. 158, 383 (1967)
N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966)
S. Coleman, Comm. Math. Phys. 31, 259 (1973)
Roger F. Dashen, Shang-keng Ma, and R. Rajaraman, this issue, Phys. Rev. D 11, 1499 (1975)

[c1] P. C. Hohenberg, Phys. Rev. 158, 383 (1967)

[c2] N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966)

[c3] S. Coleman, Comm. Math. Phys. 31, 259 (1973)

[c4] Roger F. Dashen, Shang-keng Ma, and R. Rajaraman, this issue, Phys. Rev. D 11, 1499 (1975)

Physical Review D

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Comments on the absence of spontaneous symmetry breaking in low dimensions

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