A New Formulation of a 1+1 Dimensional Field Theory Constrained to a Box

TL;DR

This paper introduces a novel formalism for 1+1 dimensional field theories in a finite box, using an analogy to finite temperature field theory, simplifying calculations of Green functions without sums or analytic continuations.

Contribution

It develops a new approach based on finite temperature field theory techniques to compute Green functions in bounded spatial domains, avoiding traditional sum and continuation methods.

Findings

Successfully calculated the self-energy in a scalar theory using the new formalism.

Demonstrated that the method simplifies the computation of spatially retarded Green functions.

Provided a framework applicable to other bounded quantum field theories.

Abstract

We consider a 1+1 dimensional field theory constrained to a finite box of length L. Traditionally, calculations in a box are done by replacing the integrals over the spatial momenta by discrete sums and then evaluating sums and doing analytic continuations. We show that it is also possible to do such calculations using an analogy to finite temperature field theory. We develop a formalism that is similar to the closed time path formulation of finite temperature field theory. Our technique can be used to calculate spatially retarded green functions, without evaluating sums or doing analytic continuations. We calculate the self energy in a simple scalar theory as an example.