Abstract:
This paper begins with some background information and a summary of results in atomic supersymmetry. The connection between the supersymmetric Coulomb and oscillator problems in arbitrary dimensions is outlined. Next, I treat the issue of finding a description of supersymmetry-based quantum-defect theory in terms of oscillators. A model with an anharmonic term that yields analytical eigenfunctions is introduced to solve this problem in arbitrary dimensions. Finally, I show that geonium atoms (particles contained in a Penning trap) offer a realization of a multidimensional harmonic oscillator in an idealized limit. The anharmonic theory presented here provides a means of modeling the realistic case.

Abstract:
In this talk, I review the possibility that CPT and Lorentz symmetry might be spontaneously broken in nature by effects originating in a theory beyond the standard model, and I discuss some existing and future experimental tests.

Abstract:
A general Lorentz-violating extension of the standard model of particle physics, allowing for both CPT-even and CPT-odd effects, is described. Some of its theoretical aspects and experimental implications are summarized.

Abstract:
A mechanism for spontaneous CPT breaking appears in string theory. Possible implications for present-energy particle models are discussed. A realistic string theory might exhibit CPT violation at levels detectable in current or future experiments. Bounds on CPT from neutral-meson oscillations are considered.

Abstract:
This talk provides an overview of a string-based mechanism for spontaneous CPT violation. A summary is given of theoretical developments. The mechanism could generate CPT-violating contributions to a four-dimensional low-energy effective theory and thereby produce detectable consequences for candidate experiments with neutral-meson systems.

Abstract:
A sketch of our results on CPT and strings is given. A mechanism for spontaneous CPT violation in string theory is briefly reviewed, and recent theoretical progress is summarized. Possible CPT-violating contributions to a four-dimensional low-energy effective theory could produce effects at levels testable in neutral-meson systems. Likely experimental signatures and attainable bounds are outlined in candidate experiments with correlated and uncorrelated neutral mesons.

Abstract:
A brief summary is given of recent developments concerning a Lorentz-violating extension of the standard model and its implications for experiments testing Lorentz and CPT symmetry.

Abstract:
This talk summarizes some theoretical features and experimental implications of a general Lorentz-violating extension of the minimal SU(3) x SU(2) x U(1) standard model that allows for both CPT-even and CPT-odd effects. The theory would arise as the low-energy limit of a fundamental theory that is Lorentz and CPT covariant but in which spontaneous Lorentz breaking occurs. The use of neutral-meson oscillations and various QED systems to bound the apparent CPT and Lorentz violations is described.

Abstract:
A short review is given of some theoretical approaches to CPT violation. A potentially realistic possibility is that small apparent breaking of CPT and Lorentz symmetry could arise at the level of the standard model from spontaneous symmetry breaking in an underlying theory. Some experimental constraints are described.

Abstract:
A general Lorentz-violating extension of the minimal SU(3) x SU(2) x U(1) standard model is described, including both CPT-even and CPT-odd terms. Some theoretical properties and experimental implications are given. The extension can be regarded as a low-energy limit of a physically relevant Lorentz-covariant fundamental theory in which spontaneous Lorentz violation occurs.