scholarly journals Stochastic Quantization Method in Operator Formalism

1983 ◽  
Vol 69 (6) ◽  
pp. 1764-1793 ◽  
Author(s):  
M. Namiki ◽  
Y. Yamanaka
Keyword(s):  
Stochastic Quantization ◽  
Quantization Method ◽  
Operator Formalism

BRST STOCHASTIC QUANTIZATION

1991 ◽  
Vol 06 (28) ◽  
pp. 4985-5015 ◽  
Author(s):  
HELMUTH HÜFFEL
Keyword(s):  
Field Theory ◽  
Particle System ◽  
Relativistic Particle ◽  
Point Particle ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Quantization Method ◽  
Second Quantization ◽  
Spinning Particle ◽  
Constrained Hamiltonian Systems

After a brief review of the BRST formalism and of the Parisi-Wu stochastic-quantization method, the BRST-stochastic-quantization scheme is introduced. This scheme allows the second quantization of constrained Hamiltonian systems in a manifestly gauge-symmetry-preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed with a discussion on the interacting field theory associated with the relativistic-point-particle system.

scholarly journals THE STOCHASTIC QUANTIZATION METHOD IN PHASE SPACE AND A NEW GAUGE FIXING PROCEDURE

1994 ◽  
Vol 09 (30) ◽  
pp. 2803-2815
Author(s):  
RIUJI MOCHIZUKI
Keyword(s):  
Phase Space ◽  
Path Integral ◽  
Equilibrium Solution ◽  
Planck Equation ◽  
Langevin Equations ◽  
Stochastic Quantization ◽  
Quantization Method ◽  
Canonical Variables ◽  
Gauge Fixing ◽  
Integral Distribution

We study the stochastic quantization of the system with first class constraints in phase space. Though the Langevin equations of the canonical variables are defined without ordinary gauge fixing procedure, gauge fixing conditions are automatically selected and introduced by imposing stochastic consistency conditions upon the first class constraints. Then the equilibrium solution of the Fokker–Planck equation is identical to the corresponding path-integral distribution.

STOCHASTIC QUANTIZATION AND 1/N EXPANSION

1993 ◽  
Vol 08 (02) ◽  
pp. 115-128
Author(s):  
J.C. BRUNELLI ◽  
R.S. MENDES
Keyword(s):  
Perturbation Theory ◽  
Sigma Model ◽  
Functional Approach ◽  
Two Dimensions ◽  
Field Theories ◽  
Nonlinear Sigma Model ◽  
Stochastic Quantization ◽  
Quantization Method ◽  
Systematic Procedure

We study the 1/N expansion of field theories in the stochastic quantization method of Parisi and Wu using the supersymmetric functional approach. This formulation provides a systematic procedure to implement the 1/N expansion which resembles the ones used in the equilibrium. The 1/N perturbation theory for the nonlinear sigma-model in two dimensions is worked out as an example.

scholarly journals Numerical Simulation of Nonlinear  -Model by Means of Stochastic Quantization Method

1985 ◽  
Vol 73 (1) ◽  
pp. 186-196 ◽  
Author(s):  
M. Namiki ◽  
I. Ohba ◽  
K. Okano ◽  
M. Rikihisa ◽  
S. Tanaka
Keyword(s):  
Numerical Simulation ◽  
Nonlinear Model ◽  
Stochastic Quantization ◽  
Quantization Method

RENORMALIZATION OF STOCHASTICALLY QUANTIZED FIELD THEORIES

1988 ◽  
Vol 03 (01) ◽  
pp. 163-185 ◽  
Author(s):  
S. CHATURVEDI ◽  
A.K. KAPOOR ◽  
V. SRINIVASAN
Keyword(s):  
Langevin Equation ◽  
Field Theories ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Coupling Constant ◽  
Operator Formalism ◽  
Four Dimensions ◽  
Quantized Field ◽  
The One ◽  
Renormalization Constants

We discuss the renormalizability of stochastically quantized ϕ4 theory in four dimensions using the operator formalism of the Langevin equation developed by Namiki and Yamanaka. The operator formalism casts the Parisi Wu stochastic quantization scheme into a five-dimensional field theory. The usefulness of this approach over the one based directly on the Langevin equation is brought out for discussion of renormalization. We propose a new regularization scheme for the stochastic diagrams and use it to compute the renormalization constants and counter terms for the ϕ4 theory to second order in the coupling constant.

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