Abstract
Apart from simple models, like those discussed in the previous section, the existence of a symmetry breaking order parameter is a non-trivial problem which in principle requires the control on the correlation functions. In this section we briefly discuss constructive criteria for symmetry breaking.
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References
J. Goldstone, Nuovo Cim. 10, 154 (1961). For a general critical discussion and for an outline of the constructive approach to symmetry breaking in quantum field theory, see A.S. Wightman, Constructive Field Theory, in Fundamental Interactions in Physics and Astrophysics, (Coral Gables 1972), G. Iverson et al. eds., Plenum 1973.
S. Coleman and E. Weinberg, Phys. Rev. D7, 1888 (1973).
B.W. Lee, Nucl. Phys. B9, 649 (1969); K. Symanzik, Renormalization of Theories with Broken Symmetry, in Cargèse Lectures in Physics 1970, D. Bessis ed., Gordon and Breach, New York 1972; C. Becchi, A. Rouet and R. Stora, Renormalizable Theories with Symmetry Breaking, in Field Theory, Quantization and Statistical Physics, E. Tirapegui ed., D. Reidel 1981. For textbook accounts, see e.g. J. Collins, Renormalization, Cambridge Univ. Press 1984, Chap. 9; L.S. Brown, Quantum Field Theory, Cambridge Univ. Press 1994.
See J. Glimm and A. Jaffe, Quantum Physics. A Functional Integral Point of View, 2nd ed., Springer 1987. For a handy account see [SNS 96].
D. Ruelle, Statistical Mechanics, Benjamin 1969. For the applications see also G.L. Sewell, Quantum Theory of Collective Phenomena, Oxford Univ. Press 1986, esp. Part III, and B. Simon, The Statistical Mechanics of Lattice Gases, Vol. I, Princeton Univ. Press 1993.
N.N. Bogoliubov, Lectures on Quantum Statistics, Vol.2, Gordon and Breach 1970, Part 1.
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Strocchi, F. (2008). Constructive Symmetry Breaking. In: Symmetry Breaking. Lecture Notes in Physics, vol 732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73593-9_20
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DOI: https://doi.org/10.1007/978-3-540-73593-9_20
Publisher Name: Springer, Berlin, Heidelberg
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