# Manifestly Finite Derivation of the Quantum Kink Mass

## TL;DR

This paper presents a new, finite derivation of the quantum kink mass in scalar field theory by directly diagonalizing the Poschl-Teller Hamiltonian, avoiding regularization issues and potentially extending to other solitons.

## Contribution

The authors introduce a method to compute the quantum kink mass using the kink operator and exact PT eigenstates, eliminating the need for regularization and compactification.

## Key findings

- Finite, regularization-free mass formula derived
- Method applicable to other quantum solitons
- Explicit diagonalization of PT Hamiltonian achieved

## Abstract

In 1974 Dashen, Hasslacher and Neveu calculated the leading quantum correction to the mass of the kink in the scalar $\phi^4$ theory in 1+1 dimensions. The derivation relies on the identification of the perturbations about the kink as solutions of the Poschl-Teller (PT) theory. They regularize the theory by placing it in a periodic box, although the kink is not itself periodic. They also require an ad hoc identification of plane wave and PT states which is difficult to interpret in the decompactified limit. We rederive the mass using the kink operator to recast this problem in terms of the PT Hamiltonian which we explicitly diagonalize using its exact eigenstates. We normal order from the beginning, rendering our theory finite so that no compactification is necessary. In our final expression for the kink mass, the form of the PT potential disappears, suggesting that our mass formula applies to other quantum solitons.