Two-Loop Scalar Kinks

TL;DR

This paper calculates the two-loop quantum correction to scalar kink masses and constructs the ground state explicitly, using a novel approach that simplifies the renormalization process in scalar field theories.

Contribution

It introduces a method to compute two-loop kink masses and states in scalar field theories with arbitrary potentials, avoiding complex regulator matching.

Findings

Two-loop kink mass explicitly calculated.

Two-loop kink ground state explicitly constructed.

Simplified renormalization using a new collective coordinate alternative.

Abstract

At one loop, quantum kinks are described by a sum of quantum harmonic oscillator Hamiltonians, and the ground state is just the product of the oscillator ground states. Two-loop kink masses are only known in integrable and supersymmetric cases and two-loop states have never been found. We find the two-loop kink mass and explicitly construct the two-loop kink ground state in a scalar field theory with an arbitrary nonderivative potential. We use a coherent state operator which maps the vacuum sector to the kink sector, allowing all states to be treated with a single Hamiltonian which needs to be renormalized only once, eliminating the need for regulator matching conditions. Our calculation is greatly simplified by a recently introduced alternative to collective coordinates, in which the kink momentum is fixed perturbatively.