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R. Mochizuki

Publications and source records attributed to R. Mochizuki.

5 recordsLinked to original sources
arXiv1993

The Stochastic Quantization Method in Phase Space and a New Gauge Fixing Procedure

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 with corresponding path integral distribution.

hep-th↗
arXiv1992

Treatment of Constraints in Stochastic Quantization Method and Covariantized Langevin Equation

We study the treatment of the constraints in stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking account of the Ito calculus. Then we obtain an improved Langevin equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochastic equilibrium state. This treatment is applied to $O(N)$ non-linear $σ$ model and it is shown that singular terms appearing in the improved Langevin equation cancel out the $δ^n(0)$ divergences in one loop order. We also ascertain that the above Langevin equation, rewritten in terms of independent variablesis, actually equivalent to the one in the general-coordinate-transformation-covariant and vielbein-rotation-invariant formalism.

hep-th↗
arXiv1992

(D+1)-Dimensional Formulation for D-Dimensional Constrained Systems

D-dimensional constrained systems are studied with stochastic Lagrangian and\break Hamiltonian. It is shown that stochastic consistency conditions are second class constraints and Lagrange multiplier fields can be determined in (D+1)-dimensional canonical formulation. The Langevin equations for the constrained system are obtained as Hamilton's equations of motion where conjugate momenta play a part of noise fields.

hep-th↗
arXiv1992

Dynamical Symmetry Breaking on Langevin Equation : Nambu $\cdot$ Jona-Lasinio Model

In order to investigate dynamical symmetry breaking, we study Nambu$\cdot$Jona-Lasinio model in the large-N limit in the stochastic quantization method. Here in order to solve Langevin equation, we impose specified initial conditions and construct ``effective Langevin equation'' in the large-N limit and give the same non-perturbative results as path-integral approach gives. Moreover we discuss stability of vacuum by means of ``effective potential''.

hep-th↗