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.
Highlights
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. 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
The one-soliton sector Hamiltonian was not normal ordered when written in terms of the eigenfunctions of its kinetic term, but commuting the corresponding creation operators to the left produced a constant term which was precisely equal to the result of ref. [1] for the one-loop correction to the mass
We used the sine-Gordon model to test the method introduced in ref. [6] for the calculation of the one-loop correction to soliton masses
Summary
Where m and λ are positive numbers. The field φ has dimensions of [action]1/2, m has dimensions of [mass] and λ has dimensions of [action]−1 the only dimensionless constant is λ. Our loop expansion will be an expansion in λ. Without loss of generality we will be interested in solitons which connect the adjacent ground states |0 0 and |0 1. The normal ordering in eq (2.1) is defined with respect to this a and a†. Let E0 and EK be the Hamiltonian eigenvalues of the vacua |0 k and the one-soliton sector ground state |K. The leading contributions appear at two loops and are of order O(λ2). We will see that they are not relevant to the one-loop soliton mass which is of order O(λ0). At the one-loop order considered here, E0 = 0. At leading order in the semiclassical expansion one expects that this will be the form factor of the soliton ground state [8].
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