Linear Spinor Field Equations for Arbitrary Spins

When utilizing a cluster decomposible relativistic scattering formalism, it is most convenient that the covariant field equations take on a linear form with respect to the energy and momentum dispersion on the fields in the manner given by the Dirac form for spin \half systems. A general spinor formulation is given for arbitrary spins by minimally extending the Lorentz algebra to include operators whose matrix representation give general Dirac matrices. The forms of these matrices are explicitly demonstrated for spin \half and spin 1 fields.Comment: 9 page

An Exploration of the Physics of Spherically Symmetric Dynamic Horizons

Geometries with horizons offer insights into relationships between general relativity and quantum physics. For static spherically symmetric space-times, the event horizon is coincident with a coordinate anomaly that introduces complications in descriptions of near horizon physics. Naive introduction of dynamics using coordinates with anomalous behavior coincident with the horizon also introduces invariant singular physical content at that horizon. However, the introduction of a temporal coordinate that is non-orthogonal to spatial coordinates near the horizon, but asymptotically orthogonal, provides a dynamic description without singular physical content at the horizon itself. Penrose diagrams will be presented exhibiting temporal dependencies for accreting and evaporating black holes, and near horizon light-like trajectories will be examined. In addition, the quantum mechanics of simple quantum fields will be explored. Finally, a two-fluid cosmology will be suggested to describe dynamic coherent aspects of the universe as a whole.Comment: Invited talk presented at the 2008 Annual Conference of the National Society of Black Physicists and National Society of Hispanic Physicists, Feb. 20-23, Washington, D.C., 37 pages, 12 figures, symbol fonts in figures correcte

An Extended Poincare Algebra for Linear Spinor Field Equations

When utilizing a cluster decomposible relativistic scattering formalism, it is most convenient that the covariant field equations take on a linear form with respect to the energy and momentum dispersion on the fields in the manner given by the Dirac form for spin ${1 \over 2}$ systems. The general spinor formulation for arbitrary spins given in a previous paper is extended to include momentum operators. Unitary quantum mechanical representations are developed for these operators, and physical interpretations are suggested.Comment: 10 pages, typos correcte

Group Structure of an Extended Lorentz Group

In a previous paper we extended the Lorentz group to include a set of Dirac boosts that give a direct correspondence with a set of generators which for spin 1/2 systems are proportional to the Dirac matrices. The group is particularly useful for developing general linear wave equations beyond spin 1/2 systems. In this paper we develop explicit group properties of this extended Lorentz group to obtain group parameters that will be useful for physical calculations for systems which might manifest the group properties. This group is a subgroup of an extended Poincare group, whose structure will be developed in a subsequent paper.Comment: 10 page

Group Structure of an Extended Poincare Group

In previous papers we extended the Lorentz and Poincare groups to include a set of Dirac boosts that give a direct correspondence with a set of generators which for spin 1/2 systems are proportional to the Dirac matrices. The groups are particularly useful for developing general linear wave equations beyond spin 1/2 systems. In this paper we develop explicit group properties of the extended Poincare group to obtain group parameters that will be useful for physical calculations in systems which manifest the group properties. The inclusion of space-time translations will allow future explorations of the gauge properties inherent in the group structure.Comment: 7 page

An Introduction of Multiple Scales in a Dynamical Cosmology

The discovery of scale acceleration evidenced from supernovae luminosities and spatial flatness of feature evolution in the cosmic microwave background presents a challenge to the understanding of the evolution of cosmological vacuum energy. Although some scenarios prefer a fixed cosmological constant with dynamics governed in a Friedman-Robertson-Walker (FRW) geometry, an early inflationary epoch remains a popular model for cosmology. It is therefore advantageous to develop a metric framework that allows a transition from an early inflationary period to a late stage dominated by dark energy. Such a metric is here developed, and some properties of this metric are explored.Comment: 8 pages, minor typo correctio

Diagonal Forms of a Dual Scale Cosmology

A hybrid metric with off-diagonal temporal-radial behavior that was constructed to conveniently parameterized the early and late time behaviors of the universe is shown to have diagonal forms consistent with Robertson-Walker and deSitter geometries. The dynamics of the energy content of the cosmology as parameterized by the classical thermal fraction is briefly discussed as motivation for the comparison of the observables predicted by various micoscopic models of the early evolution of the universe.Comment: 5 page

Linear Spinor Fields in Relativistic Dynamics

Linear spinor fields are a generalization of the Dirac field that have transparent cluster decomposability properties needed for classical correspondence of relativistic quantum systems. The algebra of these fields directly incorporate gravitation within a group that unifies the dynamics of the same number of additional hermitian carriers of quantum numbers as there are gauge fields in SU(3)$\times$SU(2)$\times$U(1). They also provide a mechanism for the dynamic mixing of massless neutrinos using a "transverse mass" conjugate to the affine parameter labeling translations along its light-like trajectory, consistent with those in the standard model.Comment: 13 page

A Model of Unified Gauge Interactions

Linear spinor fields are a generalization of the Dirac field that have direct correspondence with the known physics of fermions, inherent causality properties in their most fundamental constructions, and positive mass eigenvalues for all particle types. The algebra of the generators for infinitesimal transformations of these fields directly constructs the Minkowski metric \emph{within} the internal group space as a consequence of non-vanishing commutation relations between generators that carry space-time indexes. In addition, the generators have a fundamental matrix representation that includes Lorentz transformations within a group that unifies internal gauge symmetries generated by a set of hermitian generators for SU(3)$\times$SU(2)$\times$U(1), and nothing else. The construction of linearly independent internal SU(3) and SU(2) symmetry groups necessarily involves the mixing of three generations of the mass eigenstates labeling the (massive) representations of the linear spinor fields. The group algebra also provides a mechanism for the dynamic mixing of massless particles of differing "transverse mass" eigenvalues conjugate to the affine parameter labeling translations along their light-like trajectories. The inclusion of a transverse mass generator is necessary for group closure of the extended Poincare algebra, but its eigenvalue must vanish for massive particle representations. A unified set of space-time group transformation operations along with internal gauge group symmetry operations for linear spinor fields will be demonstrated in this paper.Comment: 11 page

A Conjecture for Using Optical Methods for Affecting Superfluid Hydrodynamics

The relation between the macroscopic quantum coherent nature of superfluids and the coherent properties of optical interference patterns will be utilized to examine the optical properties of superfluid hydrodynamics. A Bragg pattern imposed on the superfluid (either holographically or using a phase mask) is expected to induce periodic variations in the local index of refraction of the normal and super fluid components. The altered optical properties can then be probed by a second coherent light source. In this manner, the behavior of the probe beam can be switched using the specific characteristics of the imposed pattern. Acoustic modes should also manifest measurable affects on incident coherent radiations.Comment: 7 page