Equivalence of Hamiltonian and Lagrangian Path Integral Quantization

Abstract

The HLE theorem is proven for effective Lagrangians with arbitrary interactions of scalars, fermions, massless and massive vector bosons. This theorem states that the correct Hamiltonian path intergral formalism is equivalent to the convenient Lagrangian path integral ansatz. In particular, this theorem is valid for effective gauge theories, which justifies Faddeev-Popov quantization of these theories. Specific attention is paid to effective interactions of massive vector fields, which can be embedded within gauge noninvariant theories or within spontaneously broken gauge theories. These different types of models are related to each other by the Stuckelberg formalism, which is reformulated within the Hamiltonian formalism. Effective Lagrangians with higher derivatives of the fields are also considered. The HLE theorem is even valid in this case because each effective higher-order Lagrangian can be reduced to a first-order one by applying the equations of motion to the effective interaction term. This thesis is essentially a combination of previous publications of the author.