Recent years have seen a renewed interest in experimental tests of Lorentz and CPT symmetry. Observable signals of Lorentz and CPT violation can be described in a modelindependent way using effective field theory (Kostelecký and Potting, 1995). The general realistic effective field theory for Lorentz violation is called the standard-model extension (SME) (Colladay and Kostelecký, 1997; 1998; Ko...

We construct supersymmetric Lorentz violating operators for matter and gauge fields. We show that in the supersymmetric standard model the lowest possible dimension for such operators is five, and therefore they are suppressed by at least one power of an ultraviolet energy scale, providing a possible explanation for the smallness of Lorentz violation and its stability against radiative correcti...

This talk summarizes some theoretical features and experimental implications of a general Lorentz-violating extension of the minimal SU(3) × SU(2)× 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-meso...

Stokes parameters form a Minkowskian 4-vector under various optical transformations. As a consequence, the resulting two-by-two density matrix constitutes a representation of the Lorentz group. The associated Poincaré sphere is a geometric representation of the Lorentz group. Since the Lorentz group preserves the determinant of the density matrix, it cannot accommodate the decoherence process t...

We show that the hadron vector resonances are described by fields transforming according to different inequivalent representations of the Lorentz group: (1/2, 1/2) and (1, 0) + (0, 1). The vector representation (1/2, 1/2) is well studied and corresponds to the gauge fields. On the other hand, the chiral representations (1, 0) and (0, 1) are described by the second rank antisymmetric tensor fiel...

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge ‘2-group’. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an importa...

The Stokes parameters form a Minkowskian four-vector under various optical transformations. As a consequence, the resulting two-by-two density matrix constitutes a representation of the Lorentz group. The associated Poincaré sphere is a geometric representation of the Lorentz group. Since the Lorentz group preserves the determinant of the density matrix, it cannot accommodate the decoherence pr...

Dual field theory realisations are given for linearised gravity in terms of gauge fields in exotic representations of the Lorentz group. The field equations and dual representations are discussed for a wide class of higher spin gauge fields. For non-linear Einstein gravity, such transformations can be implemented locally in light-cone gauge, or partially implemented in the presence of a Killing...

Gauge fields in exotic representations of the Lorentz group in D dimensions – i.e. ones which are tensors of mixed symmetry corresponding to Young tableaux with arbitrary numbers of rows and columns – naturally arise through massive string modes and in dualising gravity and other theories in higher dimensions. We generalise the formalism of differential forms to allow the discussion of arbitrar...

Lorentz symmetry is a foundational property of modern physics, underlying the standard model of particles and general relativity. It is anticipated that these two theories are low-energy approximations of a single theory that is unified and consistent at the Planck scale. Many unifying proposals allow Lorentz symmetry to be broken, with observable effects appearing at Planck-suppressed levels; ...