Ground States of the $\phi^4$ Double-Well QFT

TL;DR

This paper computes the ground states of the 1+1 dimensional $^4$ double-well quantum field theory at second order in perturbation theory, explicitly constructing the creation operators and state interpolations.

Contribution

It provides the first explicit second-order perturbative construction of ground states and transition operators in the $^4$ double-well quantum field theory.

Findings

Explicit second-order ground state operators constructed

Operators interpolating between ground states derived

Warm-up analysis in quantum mechanics included

Abstract

At second order in perturbation theory, we find the ground states of the $\phi^4$ double-well quantum field theory in 1+1 dimensions. The operators which create these ground states from the free vacuum are constructed explicitly at this order, as is the operator which interpolates between the ground states. As a warm up we perform the analogous calculation in quantum mechanics, where the true ground state is unique but in perturbation theory there are also two ground states.