Stochastic quantization of matrix and lattice gauge models
We introduce a stochastic diffusion equation and the Fokker-Planck equation for various matrix models including the U(N) x U(N) chiral model and lattice gauge theories. It is shown how to calculate various U(N) integrals using the stochastic equation. In particular, in the external-field problem, the exact large-N result (in the weak-coupling region) is reproduced and a 1/N/sup 2/ correction is computed. Also, the order parameter is calculated up to order 1/..beta../sup 2/. In the U(N) x U(N) chiral model, the large-N reduction and quenching is done in the context of stochastic quantization, and the semiclassical results of Bars, Gunaydin, and Yankielowicz for the free energy and the two-point correlation function are derived. In lattice gauge theory, a very simple way of deriving the complete Schwinger-Dyson equations from the Fokker-Planck equation is demonstrated and, as in the chiral model, a reduced, quenched stochastic equation is derived.
- Research Organization:
- Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York 11794
- OSTI ID:
- 5752779
- Journal Information:
- Phys. Rev. D; (United States), Vol. 27:10
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
LATTICE FIELD THEORY
DIFFUSION
FOKKER-PLANCK EQUATION
GAUGE INVARIANCE
CHIRALITY
SEMICLASSICAL APPROXIMATION
STOCHASTIC PROCESSES
U GROUPS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
INVARIANCE PRINCIPLES
LIE GROUPS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
SYMMETRY GROUPS
645400* - High Energy Physics- Field Theory