Massive vector mesons and gauge theory

Abstract

We show that the requirements of renormalizability and physical consistency imposed on perturbative interactions of massive vector mesons fix the theory essentially uniquely. In particular, physical consistency demands the presence of at least one additional physical degree of freedom which was not part of the originally required physical particle content. In its simplest realization (probably the only one) these are scalar fields as envisaged by Higgs but in the present formulation without the `symmetry-breaking Higgs condensate'. The final result agrees precisely with the usual quantization of a classical gauge theory by means of the Higgs mechanism. However, the emphasis is shifted: instead of invoking the gauge principle (and the Higgs mechanism) on the local quantum field theory, the principles of local quantum physics restricted by the perturbative renormalizability demand `explains' (via Bohr's correspondence) the classical gauge principle as a selection principle among the many a priori (semi)classical possibilities of coupling vector fields among each other. Our method proves an old conjecture of Cornwall, Levin and Tiktopoulos stating that the renormalization and consistency requirements of spin-1 particles lead to the gauge theory structure (i.e. a kind of inverse of 't Hooft's famous renormalizability proof in quantized gauge theories) which was based on the on-shell unitarity of the S-matrix. Since all known methods of renormalized perturbation theory are off-shell, our proof is different and a bit more involved than the original arguments. We also speculate on a possible future ghost-free formulation which avoids `field coordinates' altogether and is expected to reconcile the on-shell S-matrix point of view with the off-shell field theory structure.