The stochastic quantisation of U(N) and SU(N) lattice gauge theory and Langevin equations for the Wilson loops

ALDAZABAL, G.; GONZALEZ-ARROYO, A.; PARGA, N.

JOURNAL OF PHYSICS. A - MATHEMATICAL AND GENERAL

IOP

Año: 1985 vol. 18 p. 2975 - 2993

0305-4470

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.