Nonperturbative Stochastic Quantization of the Helix Model

Abstract

The helix model describes the minimal coupling of an abelian gauge field with three bosonic matter fields in 0+1 dimensions; it is a model without a global Gribov obstruction. We perform the stochastic quantization in configuration space and prove nonperturbatively equivalence with the path integral formalism. Major points of our approach are the geometrical understanding of separations into gauge independent and gauge dependent degrees of freedom as well as a generalization of the stochastic gauge fixing procedure which allows to extract the equilibrium Fokker-Planck probability distribution of the model.Comment: 43 pages, LaTex, 1 encapsulated Postscript figure (epsbox.sty) include

Cooper Pair Formation by Quantizing Brownian Motion

“…Then, as a benefit, it gains new insights for correct nonpertubative path integral formulation of gauge theories [12]. Consistency with conventional quantum field theory like QED and Yang-Mills field was found in several explicit examples [13,14].…”

Generalized stochastic gauge fixing

“…We see that the new drift term clearly is not acting tangential to the gauge orbit; its rather complicated structure is necessary for leaving unchanged gauge invariant expectation values; the straightforward proof is given in [5].…”

“…We present now our generalization [5] of Zwanziger's stochastic gauge fixing procedure by adding a specific drift term which not only has tangential components along the gauge orbits; in addition we modify the Wiener process itself. In this way we introduce more than just one function α , in fact we add m additional functions β i appearing in the drift term as well as in the Wiener process part of the Langevin equation.…”

Field space entanglement entropy, zero modes and Lifshitz models

“…Expectation values of gauge invariant observables again remain untouched. With [46,43] a well defined Fokker-Planck formulation with normalizable ground state is obtained and the corresponding Lifshitz model can be derived in a consistent way. As a consequence the issue of comparing field space entanglement entropies of quantum field theories and of their Lifshitz duals can be addressed.…”