Prog. Theor. Phys. Vol. 72 No. 2 (1984) pp. 350-365

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Sthochastic Quantization of Constrained Systems

— General Theory and Nonlinear Sigma Model —

Mikio Namiki, Ichiro Ohba and Keisuke Okano

Department of Physics, Waseda University, Tokyo 160

(Received March 30, 1984)

Abstract:

The stochastic quantization method is extended to a dynamical system described by regular Lagrangian under additional holonomic constraints. We first show that the stochastic quantization method surely yields the same result as given by the path-integral quantization, by imposing the constraints on the system throughout the whole hypothetical stochastic process with respect to a fictitious time. Next we propose, on the analogy of the theory of optimization, new types of rather moderate constraints, (i) converging constraints and (ii) fluctuating constraints, which are so desined as to coincide with the original ones only at the infinite fictitious-time limit. The present formalism with the new types of constraints prepares a feasible method to carry out numerical analyses of a dynamical system with nonlinear constraints. We can expect that the method works well in the case of the lattice nonlinear σ-model.

URL : http://ptp.ipap.jp/link?PTP/72/350/
DOI : 10.1143/PTP.72.350

References:

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Citing Article(s) :

Progress of Theoretical Physics Vol. 73 No. 1 (1985) pp. 186-196 :
Numerical Simulation of Nonlinear σ-Model by Means of Stochastic Quantization Method

Mikio Namiki, Ichiro Ohba, Keisuke Okano, Masanori Rikihisa and Satoshi Tanaka
Progress of Theoretical Physics Vol. 75 No. 6 (1986) pp. 1447-1459 :
Complete Renormalization Scheme for Fictitious-Time Correlations in Stochastic Quantization Method Based on Operator Formalism

Mikio Namiki and Yoshiya Yamanaka
Progress of Theoretical Physics Vol. 76 No. 2 (1986) pp. 501-511 :
New Procedure of Numerical Simulation of Long-Range Correlations and Energy Gaps by Stochastic Quantization

Mikio Namiki, Ichiro Ohba, Keisuke Okano, Masanori Rikihisa and Satoshi Tanaka
Progress of Theoretical Physics Vol. 77 No. 5 (1987) pp. 1267-1285 :
Stochastic Quantization of System under Constraints through Phase Space Formulation

Ichiro Ohba
Progress of Theoretical Physics Vol. 86 No. 5 (1991) pp. 1053-1075 :
BRS Symmetry in Stochastic Quantization of Gravity

Naohito Nakazawa
Progress of Theoretical Physics Vol. 88 No. 6 (1992) pp. 1233-1238 :
(D + 1)-Dimensional Formulation for D-Dimensional Constrained Systems

Riuji Mochizuki
Progress of Theoretical Physics Supplement No.111 (1993) pp. 53-62 :
Stochastic Quantization of Constrained Systems

Ichiro Ohba
Progress of Theoretical Physics Supplement No.111 (1993) pp. 203-236 :
Renormalization in Stochastic Quantization and Supersymmetry

Keisuke Okano