Finite derivation of the one-loop sine-Gordon soliton mass

Abstract

Calculations of quantum corrections to soliton masses generally require both the vacuum sector and the soliton sector to be regularized. The finite part of the quantum correction depends on the assumed relation between these regulators when both are taken to infinity. Recently, in the case of quantum kinks, a manifestly finite prescription for the calculation of the quantum corrections has been proposed, which uses the kink creation operator to relate the two sectors. In this note, we test this new prescription by calculating the one-loop correction to the Sine-Gordon soliton mass, reproducing the well-known result which has been derived using integrability. * guohengyuan@impcas.ac.cn

Constructing Quantum Soliton States Despite Zero Modes

“…In Ref. [23] we solved Eq. (2.8) at one loop, providing an explicit expression for O|Ω at one loop in Ref.…”

“…The operator : O : b will be ordered so that when decomposed in terms of φ 0 , π 0 , b † and b, all b † and φ 0 are on the left. The Hamiltonian (2.1) was defined in terms of a normal ordering, and the mismatch between the two normal-ordering schemes is responsible for the one-loop correction to the mass [21,23]. We will refer to :: b as soliton normal ordering.…”

The Ground State of the Sine-Gordon Soliton

“…It was shown in Ref. [6] that O is equal to the identity plus quantum corrections and so (1.8) can be solved in perturbation theory. In this paper we will work at one-loop.…”

Normal ordering normal modes

“…The terms at these leading orders are given in this example in Ref. [19], and more generally are of the form (2.21). In particular they include no interactions and the tadpole vanishes in the full expression.…”