GAUGE TRANSFORMATION PROPERTIES OF VECTOR AND TENSOR POTENTIALS REVISITED: A GROUP QUANTIZATION APPROACH

Abstract

The possibility of nontrivial representations of the gauge group on wave functionals of a gauge invariant quantum field theory leads to a generation of mass for intermediate vector and tensor bosons. The mass parameters m show up as central charges in the algebra of constraints, which then become of second-class nature. The gauge group coordinates acquire dynamics outside the null-mass shell and provide the longitudinal field degrees of freedom that massless bosons need to form massive bosons. This is a non-Higgs mechanism that could provide new clues for the best understanding of the symmetry breaking mechanism in unified field theories. A unified quantization of massless and massive non-Abelian Yang–Mills, linear gravity and Abelian two-form gauge field theories are fully developed from this new approach, where a cohomological origin of mass is pointed out.