"Tunneling" Amplitudes of a Massless Quantum Field

TL;DR

The paper introduces an approximate method to compute the Green function of a massless scalar field in the presence of potential barriers, relevant for understanding tunneling phenomena in quantum field theory.

Contribution

It presents a novel approach to approximate Green functions with potential barriers of specific shapes and sizes, incorporating constraints in the functional integral framework.

Findings

Derived an expression for the Green function involving a double Fourier transform.

Applied the method to barriers with particular potential forms.

Provided insights into tunneling amplitudes in quantum fields.

Abstract

We propose a method for the approximate computation of the Green function of a scalar massless field subjected to potential barriers of given size and shape in spacetime. The potential of the barriers has the form V(phi)=xi(phi^2-phi_0^2)^2; xi is very large and phi_0 very close to zero, the product (xi phi_0^2) being finite and small. This is equivalent to the insertion of a suitable constraint in the functional integral for phi. The Green function contains a double Fourier transform of the characteristic function of the region where the potential has support.