Quantum interactions between nonperturbative vacuum fields

Abstract

We develop an approach to investigate the nonperturbative dynamics of quantum field theories, in which specific vacuum field fluctuations are treated as the low-energy dynamical degrees of freedom, while all other vacuum field configurations are explicitly integrated out from the path integral. We show how to compute the effective interaction between the vacuum field degrees of freedom both perturbatively (using stochastic perturbation theory) and fully nonperturbatively (using lattice field theory simulations). The present approach holds to all orders in the couplings and does not rely on the semiclassical approximation.

Computing the effective Hamiltonian of low-energy vacuum gauge fields

“…Ref. [5,10] ) one arrives to an expression in the form of Eq. ( 3), where the effective Hamiltonian H(γ 1 , .…”

“…Indeed, in Ref. [10] it was shown that once the system of Eq.s (11) is satisfied in one gauge, it holds also in any other gauge.…”

“…In order to tackle this problem, in a recent work we have developed a technique, which we shall refer to as Vacuum Manifold Projection (VMP), by which lattice simulations are used to rigorously compute the effective Hamiltonian of arbitrary vacuum models [10], in a model independent way. This is done by non-perturbatively performing the path integral over all the vacuum field configurations which are not explicitly taken into account in the given low-energy vacuum model.…”

“…In our first work, the VMP method was illustrated and tested by evaluating the instanton-antinstanton interaction in a simple quantum-mechanical toy model [10]. Here, we present the first application to a gauge theory.…”

Quantum effective action of multi-instanton configurations from lattice field theory

“…ones based on different types of vacuum field configurations. The details of the method briefly illustrated here will be presented in a forthcoming paper [4].The extension of the present formalism to QCD is presently in progress.…”