Diagonalizability of the longitudinal sector of the functional integral in massive SU (2) Yang–Mills theories via topological contributions

Abstract

The problem of longitudinal sector diagonalizability of the functional integral in massive SU (2) Yang–Mills theories is revisited. A new decomposition law of a massive SU (2) vector field into transverse and longitudinal parts is proposed which takes into account the more recently discovered topological properties of SU (2) gauge theories. After establishing the credibility of this decomposition law, it is shown how it leads to the diagonalizability of the longitudinal sector of the functional integral. This result is related to the problem of the existence of the zero-mass limit in massive SU (2) Yang–Mills theories.