Stochastic quantization of matrix and lattice gauge models

Journal Article · Sun May 15 04:00:00 EDT 1983 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.27.2412· OSTI ID:5752779

Guha, A; Lee, S

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), Journal Name: Phys. Rev. D; (United States) Vol. 27:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRALITY
DIFFERENTIAL EQUATIONS
DIFFUSION
EQUATIONS
FIELD THEORIES
FOKKER-PLANCK EQUATION
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LATTICE FIELD THEORY
LIE GROUPS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
SEMICLASSICAL APPROXIMATION
STOCHASTIC PROCESSES
SYMMETRY GROUPS
U GROUPS