Modal expansions and non-perturbative quantum field theory in Minkowski space

TL;DR

This paper presents a spectral approach to non-perturbative quantum field theory in Minkowski space, demonstrating calculations of propagators and proposing new computational methods for large Fock spaces.

Contribution

It introduces a spectral formalism for non-perturbative field theory and develops quasi-sparse eigenvector algorithms for large-scale Fock space computations.

Findings

Calculated real and imaginary parts of propagators in 1+1D phi^4 theory

Identified one-particle and multi-particle contributions

Discussed computational limits and proposed new eigenvector methods

Abstract

We introduce a spectral approach to non-perturbative field theory within the periodic field formalism. As an example we calculate the real and imaginary parts of the propagator in 1+1 dimensional phi^4 theory, identifying both one-particle and multi-particle contributions. We discuss the computational limits of existing diagonalization algorithms and suggest new quasi-sparse eigenvector methods to handle very large Fock spaces and higher dimensional field theories.