Hamiltonian Quantization of Effective Lagrangians with Massive Vector Fields

Abstract

Effective Lagrangians containing arbitrary interactions of massive vector fields are quantized within the Hamiltonian path integral formalism. It is proven that correct Hamiltonian quantization of these models yields the same result as naive Lagrangian quantization (Matthews's theorem). This theorem holds for models without gauge freedom as well as for (linearly or nonlinearly realized) spontaneously broken gauge theories. The Stueckelberg formalism, a procedure to rewrite effective Lagrangians in a gauge invariant way, is reformulated within the Hamiltonian formalism as a transition from a second class constrained theory to an equivalent first class constrained theory. The relations between linearly and nonlinearly realized spontaneously broken gauge theories are discussed. The quartically divergent Higgs self interaction is derived from the Hamiltonian path integral.