Matthews' theorem in effective Yang-Mills theories

Abstract

We study the quantization of effective Yang-Mills theories within the path integral formalism. In particular, the equivalence of the Hamiltonian and Lagrangian path integral quantization (Matthews' theorem) is probed for an effective Yang-Mills Lagrangian without matter fields, which includes all the invariant terms up to dimension six. This theorem is probed from point of views of both the gauge and BRST symmetries. The importance of the BRST symmetry in probing this theorem is stressed. We found that the functional integration on the generalized momenta are of Gaussian type and that they do not contribute to physical quantities as a consequence of the symmetries of the effective Lagrangian, which leads to a Lorentz and BRST invariant Lagrangian path integral.