Spontaneous Breakdown of Symmetry in Stochastic Quantization : Particles and Fields
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概要
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It is shown that the stochastic quantization method of Parisi and Wu determines the vacuum structure of the spontaneously broken theories by the stochastic Schwinger-Dyson equation which, in the equilibrium limit, reduces to the ordinary Schwinger-Dyson equation and is solved in &plank;-expansion of the contributing stochastic diagrams. The method explains the nonanalytic behavior, or the two-valuedness of order parameter at vanishing source. It incidentally avoids the problem of complexity and convexity of the effective potential in a totally different manner. The stochastic Schwinger-Dyson equation for the growing order parameter is explicitly solved in some simple cases including a λφ^4 theory with both unbroken and spontaneously broken potentials, the Goldstone and the Nambu-Jona-Lasinio models in the lowest order approximation. Ward-Takahashi identities in the spontaneously broken theories are also derived using the Langevin equation without recourse to the path-integral nor the operator formalisms.
- 理論物理学刊行会の論文
- 1992-01-25
著者
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Ito Masatoshi
Department Of Applied Mathematics Faculty Of Science Science University Of Tokyo
-
Morita Katsusada
Department Of Physics Dalhousie University Halifax : Nagoya University
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MORITA Katsusada
Department of Physics, Faculty of Science, Nagoya University
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