Gauge Invariance and the Pauli-Villars Regulator in Lorentz- and CPT-Violating Electrodynamics

We examine the nonperturbative structure of the radiatively induced Chern-Simons term in a Lorentz- and CPT-violating modification of QED. Although the coefficient of the induced Chern-Simons term is in general undetermined, the nonperturbative theory appears to generate a definite value. However, the CPT-even radiative corrections in this same formulation of the theory generally break gauge invariance. We show that gauge invariance may yet be preserved through the use of a Pauli-Villars regulator, and, contrary to earlier expectations, this regulator does not necessarily give rise to a vanishing Chern-Simons term. Instead, two possible values of the Chern-Simons coefficient are allowed, one zero and one nonzero. This formulation of the theory therefore allows the coefficient to vanish naturally, in agreement with experimental observations.Comment: 8 page

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

Conductance through an array of quantum dots

We propose a simple approach to study the conductance through an array of $N$ interacting quantum dots, weakly coupled to metallic leads. Using a mapping to an effective site which describes the low-lying excitations and a slave-boson representation in the saddle-point approximation, we calculated the conductance through the system. Explicit results are presented for N=1 and N=3: a linear array and an isosceles triangle. For N=1 in the Kondo limit, the results are in very good agreement with previous results obtained with numerical renormalization group (NRG). In the case of the linear trimer for odd $N$, when the parameters are such that electron-hole symmetry is induced, we obtain perfect conductance $G_0=2e^2/h$. The validity of the approach is discussed in detail.Comment: to appear in Phys. Rev.