Significance of constraints associated with Green’s functions in Hamiltonian perturbation theory
Tóm tắt
In many formulations of Hamiltonian perturbation theory a Green’s function becomes undefined when some parameter is allowed to vanish. Here various examples are discussed to illustrate this phenomenon, and it is shown that they are all realizations of a general theorem. The cases considered are examples in classical mechanics, quantum mechanics, electrodynamics and field theory. The prime object is to illustrate the unity of the examples and thus to make the application of the procedure to field theory models of current interest more transparent. One example that we refer to is the skyrmion model.
Tài liệu tham khảo
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G. Jona-Lasinio:Nuovo Cimento,34, 1790 (1964);G. Gilbert:Phys. Rev. Lett.,12, 713 (1964). Simple discussion of the Goldstone theorem can be found in modern books on field theory,e.g. K. Huang:Quarks, Leptons and Gauge Fields (World Scientific, Singapore, 1982).
H. J. W. Müller-Kirsten andA. Wiedemann:Nuovo Cimento A,78, 61 (1983);Phys. Lett. B,132, 169 (1983);J. Math. Phys. (N. Y.),26, 1680 (1985).
H. J. W. Müller-Kirsten andA. Wiedemann:Fortschr. Phys.,32, 281 (1984).
E. Tomboulis:Phys. Rev. D,12, 1678 (1975),N. H. Christ andT. D. Lee:Phys. Rev. D,12, 1606 (1975);L. Maharana andH. J. W. Müller-Kirsten:Nuovo Cimento A,83, 229 (1984).
E. Merzbacher:Quantum Mechanics, 2nd edition (John Wiley, New York, N. Y., 1975), Sect. 17.2. The theorem is also known as Fredholm alternative; seeB. Booss andD. D. Bleecker:Topology and Analysis (Springer, New York, N. Y., 1985), p. 26.
See,e.g.,H. J. W. Müller-Kirsten:Phys. Rev. D,22, 1952 (1980).
B. Felsager:Geometry, Particles and Fields (Odense University Press, Odense, 1981), p. 101.
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Formulae of this section can be obtained by dimensional reduction from corresponding formulae for a (1 + 1)-dimensional field theory; see,e.g.,H. J. W. Müller-Kirsten andA. Wiedemann:Dirac quantization of a supersymmetric field theory, Z. Phys. C (1987) (to appear). For the general procedure seeH. J. W. Müller-Kirsten andA. Wiedemann:Supersymmetry, an Introduction with Conceptual and Calculational Details (World Scientific, Singapore, to appear).
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