Vector Superfields and Lorentz Violation

We extend Lorentz-violating Supersymmetry models to include vector superfields. The CPT-preserving model generalizes easily, while the obvious attempt at generalizing the CPT-violating model meets serious obstructions. Generalizations of the CPT-preserving but Lorentz-Violating model to higher dimensions are also straightforward. Compactification is used to reduce the six-dimensional theory to an ${\cal{N}} =2$ Lorentz-violating theory in four dimensions, while the ten-dimensional theory is used to produce an ${\cal{N}}=4$ Lorentz-violating theory. This may be useful in future constructions involving Ads/CFT correspondence with Lorentz violation.Comment: 5 pages, submitted to Physical Review

Nonrelativisitic Ideal Gasses and Lorentz Violations

We develop statistical mechanics for a nonrelativisitic ideal gas in the presence of Lorentz violating background fields. The analysis is performed using the Standard-Model Extension (SME). We derive the corresponding laws of thermodynamics and find that, to lowest order in Lorentz violation, the scalar thermodynamic variables are corrected by a rotationally invariant combination of the Lorentz terms which can be interpreted in terms of a (frame dependent) effective mass. We find that spin couplings can induce a temperature independent polarization in the gas that is not present in the conventional case.Comment: 6 pages, proceedings for CPT and Lorentz Symmetry, Bloomington, IN, 200

Deformed Instantons

In this talk, instantons are discussed in the presence of Lorentz violation. Conventional topological arguments are applied to classify the modified solutions to the Yang-Mills equations according to the topological charge. Explicit perturbations to the instantons are calculated in detail for the case of unit topological charge.Comment: 6 pages, proceedings for CPT and Lorentz Symmetry, Bloomington, IN, 200

Lorentz Violation and Extended Supersymmetry

We construct a collection of Lorentz violating Yang-Mills theories exhibiting supersymmetry.Comment: Presented at the Fifth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 28-July 2, 201

Cherenkov radiation with massive, CPT-violating photons

The source of CPT violation in the photon sector of the Standard Model Extension arises from a Chern-Simons-like contribution that involves a coupling to a fixed background vector field k(AF)(mu). These Lorentz- and CPT-violating photons have well-known theoretical issues that arise from missing states at low momenta when k(AF)(mu) is timelike. In order to make the theory consistent, a tiny mass for the photon can be introduced, well below current experimental bounds. The implementation of canonical quantization can then be implemented as in the CPT-preserving case by using the Stuckelberg mechanism. We explicitly construct a covariant basis of properly normalized polarization vectors at fixed three-momentum satisfying the momentum space field equations, in terms of which the vector field can be expanded. As an application of the theory, we calculate the Cherenkov radiation rate for the case of purely timelike k(AF)(mu) and find a radiation rate at high energies that has a contribution that does not depend on the mass used to regulate the photons

Quaternionic Formulation of the Dirac Equation

The Dirac equation with Lorentz violation involves additional coefficients and yields a fourth-order polynomial that must be solved to yield the dispersion relation. The conventional method of taking the determinant of $4\times 4$ matrices of complex numbers often yields unwieldy dispersion relations. By using quaternions, the Dirac equation may be reduced to $2 \times 2$ form in which the structure of the dispersion relations become more transparent. In particular, it is found that there are two subsets of Lorentz-violating parameter sets for which the dispersion relation is easily solvable. Each subset contains half of the parameter space so that all parameters are included.Comment: Presented at the Fifth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 28-July 2, 201

Gupta-Bleuler Photon Quantization in the SME

Photon quantization is implemented in the standard model extension (SME) using the Gupta-Bleuler method and BRST concepts. The quantization prescription applies to both the birefringent and non-birefringent CPT-even couplings. A curious incompatibility is found between the presence of the Lorentz-violating terms and the existence of a nontrivial conjugate momentum $\Pi^0$ yielding problems with covariant quantization procedure. Introduction of a mass regulator term can avoid the vanishing of $\Pi^0$ and allows for the implementation of a covariant quantization procedure. Field-theoretic calculations involving the SME photons can then be performed using the mass regulator, similar to the conventional procedure used in electrodynamics for infrared-divergence regulation.Comment: 13 page

Bose-Einstein Condensates as a Probe for Lorentz Violation

The effects of small Lorentz-violating terms on Bose-Einstein condensates are analyzed. We find that there are changes to the phase and shape of the ground-state wave function that vary with the orientation of the trap. In addition, spin-couplings can act as a source for spontaneous symmetry breaking in ferromagnetic condensates making them sensitive probes for fundamental symmetry violation