The Stochastic Quantization of U($N$) and SU($N$) Lattice Gauge Theory and Langevin Equations for the Wilson Loops

Aldazabal, G.; Gonzalez-Arroyo, Antonio; Parga, N.

doi:10.1088/0305-4470/18/15/023

The Stochastic Quantization of U( $N$ ) and SU( $N$ ) Lattice Gauge Theory and Langevin Equations for the Wilson Loops

Jun, 1983

37 pages

Published in:

J.Phys.A 18 (1985) 2975-2993

DOI:

10.1088/0305-4470/18/15/023

Report number:

Print-83-0498 (BARILOCHE)

View in:

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Abstract: (IOP)

The authors perform the stochastic quantisation of U(N) and SU(N) lattice gauge theories. For N=1 and 2 the stochastic motion on the circle and the sphere S3 is studied while the generalisation for any N is achieved by imposing the unitarity constraints by means of Lagrange multipliers. The Langevin equations are found for the Wilson loops and it is shown that when averaged over the random forces and the new time dimension is taken to infinity they become the Schwinger-Dyson equations of the corresponding gauge theory.

LATTICE FIELD THEORY
GAUGE FIELD THEORY: U(N)
GAUGE FIELD THEORY: SU(N)
QUANTIZATION: STOCHASTIC
GAUGE FIELD THEORY: WILSON LOOP
LANGEVIN EQUATION
DYSON-SCHWINGER EQUATION

References(8)

Figures(0)

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The Stochastic Quantization of U(NNN) and SU(NNN) Lattice Gauge Theory and Langevin Equations for the Wilson Loops