Local Casimir Energy For Solitons

Direct calculation of the one-loop contributions to the energy density of bosonic and supersymmetric phi-to-the-fourth kinks exhibits: (1) Local mode regularization. Requiring the mode density in the kink and the trivial sectors to be equal at each point in space yields the anomalous part of the energy density. (2) Phase space factorization. A striking position-momentum factorization for reflectionless potentials gives the non-anomalous energy density a simple relation to that for the bound state. For the supersymmetric kink, our expression for the energy density (both the anomalous and non-anomalous parts) agrees with the published central charge density, whose anomalous part we also compute directly by point-splitting regularization. Finally we show that, for a scalar field with arbitrary scalar background potential in one space dimension, point-splitting regularization implies local mode regularization of the Casimir energy density.Comment: 18 pages. Numerous new clarifications and additions, of which the most important may be the direct derivation of local mode regularization from point-splitting regularization for the bosonic kink in 1+1 dimension

The Radiative Corrections to the Mass of the Kink Using an Alternative Renormalization Program

In this paper we compute the radiative correction to the mass of the kink in $\phi^4$ theory in 1+1 dimensions, using an alternative renormalization program. In this newly proposed renormalization program the breaking of the translational invariance and the topological nature of the problem, due to the presence of the kink, is automatically taken into account. This will naturally lead to uniquely defined position dependent counterterms. We use the mode number cutoff in conjunction with the above program to compute the mass of the kink up to and including the next to the leading order quantum correction. We discuss the differences between the results of this procedure and the previously reported ones.Comment: 8 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:0806.036