Mean field approximations for U(N) and SU(N) lattice gauge theories

Publisher Website
Google Scholar
Abstract
A particular parametrization of the groups U(N) and SU(N) is constructed by observing that the sphere S2N−1 is homeomorphic to the factor spaces U(N)/U(N−1) or SU(N)/SU(N−1) and continuing the corresponding fibration. The spheres are naturally embedded into Euclidean spaces and thus allow an extension of the mean field approximation by a saddle‐point method to U(N) and SU(N) lattice gauge theories. It differs from the standard variational approach, the result of which can also be obtained by embedding the group into the Euclidean space of matrices. For both approaches the phase transition points are calculated and compared with the results of Monte‐Carlo simulations. The best agreement is obtained for the standard variational approach with axial gauge fixing.