Abstract
We develop a method to compute the vacuum polarization energy for coupled scalar fields with different masses scattering off a background potential in one space dimension. As an example we consider the vacuum polarization energy of a kink-like soliton built from two real scalar fields with different mass parameters.
Highlights
Many nonlinear field theories allow for localized field configurations that are stable due to their topological properties or, when they possess nontrivial conserved quantum numbers, because they are energetically favored over trivial configurations with the same quantum numbers
Spectral methods [4] have proven efficient at handling these divergences, by computing the vacuum polarization energies (VPEs) from scattering data of the potential generated by the soliton and identifying the divergences from the corresponding Born series
We have generalized the spectral methods for computing the VPE of static solitons to models containing coupled fields with different mass parameters
Summary
Many nonlinear field theories allow for localized field configurations that are stable due to their topological properties or, when they possess nontrivial conserved quantum numbers, because they are energetically favored over trivial configurations with the same quantum numbers. Spectral methods [4] have proven efficient at handling these divergences, by computing the VPE from scattering data of the potential generated by the soliton and identifying the divergences from the corresponding Born series The latter is expressed as a series of Feynman diagrams that are regularized and renormalized by techniques common in perturbative quantum field theory. Within that gap it is important to ensure that the wave function of the heavier particle decreases exponentially towards spatial infinity In view of these obvious obstacles it is the main objective of the present investigation to establish a comprehensive scattering formalism for the VPE in this case, where we generalize Eq (1).
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