One-loop kink mass shifts: A computational approach

Abstract

In this paper we develop a procedure to compute the one-loop quantum correction to the kink masses in generic ( 1 + 1 ) -dimensional one-component scalar field theoretical models. The procedure uses the generalized zeta function regularization method helped by the Gilkey–de Witt asymptotic expansion of the heat function via Mellinʼs transform. We find a formula for the one-loop kink mass shift that depends only on the part of the energy density with no field derivatives, evaluated by means of a symbolic software algorithm that automates the computation. The improved algorithm with respect to earlier work in this subject has been tested in the sine-Gordon and λ ( ϕ ) 2 4 models. The quantum corrections of the sG-soliton and λ ( ϕ 4 ) 2 -kink masses have been estimated with a relative error of 0.00006% and 0.00007% respectively. Thereafter, the algorithm is applied to other models. In particular, an interesting one-parametric family of double sine-Gordon models interpolating between the ordinary sine-Gordon and a re-scaled sine-Gordon model is addressed. Another one-parametric family, in this case of ϕ 6 models, is analyzed. The main virtue of our procedure is its versatility: it can be applied to practically any type of relativistic scalar field models supporting kinks.