A Chiral Spin Theory in the Framework of an Invariant Evolution Parameter Formalism

We present a formulation for the construction of first order equations which describe particles with spin, in the context of a manifestly covariant relativistic theory governed by an invariant evolution parameter; one obtains a consistent quantized formalism dealing with off-shell particles with spin. Our basic requirement is that the second order equation in the theory is of the Schr\"{o}dinger-Stueckelberg type, which exhibits features of both the Klein-Gordon and Schr\"{o}dinger equations. This requirement restricts the structure of the first order equation, in particular, to a chiral form. One thus obtains, in a natural way, a theory of chiral form for massive particles, which may contain both left and right chiralities, or just one of them. We observe that by iterating the first order system, we are able to obtain second order forms containing the transverse and longitudinal momentum relative to a time-like vector $t_{\mu}t^{\mu}=-1$ used to maintain covariance of the theory. This time-like vector coincides with the one used by Horwitz, Piron, and Reuse to obtain an invariant positive definite space-time scalar product, which permits the construction of an induced representation for states of a particle with spin. We discuss the currents and continuity equations, and show that these equations of motion and their currents are closely related to the spin and convection parts of the Gordon decomposition of the Dirac current. The transverse and longitudinal aspects of the particle are complementary, and can be treated in a unified manner using a tensor product Hilbert space. Introducing the electromagnetic field we find an equation which gives rise to the correct gyromagnetic ratio, and is fully Hermitian under the proposed scalar product. Finally, we show that the original structure of Dirac'sComment: Latex, 61 pages. Minor revisions. To be published in J. Math. Phy

Gravitational Repulsion within a Black-Hole using the Stueckelberg Quantum Formalism

We wish to study an application of Stueckelberg's relativistic quantum theory in the framework of general relativity. We study the form of the wave equation of a massive body in the presence of a Schwarzschild gravitational field. We treat the mathematical behavior of the wavefunction also around and beyond the horizon (r=2M). Classically, within the horizon, the time component of the metric becomes spacelike and distance from the origin singularity becomes timelike, suggesting an inevitable propagation of all matter within the horizon to a total collapse at r=0. However, the quantum description of the wave function provides a different understanding of the behavior of matter within the horizon. We find that a test particle can almost never be found at the origin and is more probable to be found at the horizon. Matter outside the horizon has a very small wave length and therefore interference effects can be found only on a very small atomic scale. However, within the horizon, matter becomes totally "tachionic" and is potentially "spread" over all space. Small location uncertainties on the atomic scale become large around the horizon, and different mass components of the wave function can therefore interfere on a stellar scale. This interference phenomenon, where the probability of finding matter decreases as a function of the distance from the horizon, appears as an effective gravitational repulsion.Comment: 20 pages, 6 figure

The benthic macrofauna of sludge-affected sediments in the Derwent Estuary, southern Tasmania

The paper reports the findings of an extensive survey of benthic invertebrates from the Derwent estuary in southern Tasmania, sampled during an investigation into the distribution and character of sludge emanating from a pulp and paper factory. In total, 45 invertebrate species were collected, but none was found in the sediment in the river channel between the pulpmill (its effluent outfall) and a site 5 km downstream. Similarly, other sediments with wood fibre present (measured by loss on ignition) and with very negative redox values were faunistically depauperate and possessed much lower species richness than that anticipated from other studies in Australia. The sediments in shallow areas in the middle part of the estuary had very high densities of invertebrates and had less mechanical wood fibre than sediments in deeper water nearby or other sediments further downstream. These results suggest that smothering by wood fibre, with concomitant toxicological effects of chemical reactions in the sediment, results in the low invertebrate diversities observed. These findings must be tempered by the methodological limitations involved with the selection of sample sites and lack of seasonal data, which have prevented definitive statements from being made about the level of environmental stress being experienced in the lower parts of the estuary

Microcanonical Ensemble and Algebra of Conserved Generators for Generalized Quantum Dynamics

It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a statistical approximation to an underlying generalized quantum dynamics. This result was obtained by an argument based on a Ward identity analogous to the equipartition theorem of classical statistical mechanics. We construct here a microcanonical ensemble which forms the basis of this canonical ensemble. This construction enables us to define the microcanonical entropy and free energy of the field configuration of the equilibrium distribution and to study the stability of the canonical ensemble. We also study the algebraic structure of the conserved generators from which the microcanonical and canonical ensembles are constructed, and the flows they induce on the phase space.Comment: Plain TeX, 18 pages. Corrected report number onl

Optical modeling of agricultural fields and rough-textured rock and mineral surfaces

Review was made of past models for describing the reflectance and/or emittance properties of agricultural/forestry and geological targets in an effort to select the best theoretical models. An extension of the six parameter Allen-Gayle-Richardson model was chosen as the agricultural plant canopy model. The model is used to predict the bidirectional reflectance of a field crop from known laboratory spectra of crop components and approximate plant geometry. The selected geological model is based on Mie theory and radiative transfer equations, and will assess the effect of textural variations of the spectral emittance of natural rock surfaces

Quantum Time and Spatial Localization: An Analysis of the Hegerfeldt Paradox

Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's theory of constraints. A parametrization invariant formulation is obtained by introducing time and energy operators for the relativistic particle and then treating the Klein-Gordon equation as a constraint. The standard, physical Hilbert space is recovered, via integration over proper time, from an augmented Hilbert space wherein time and energy are dynamical variables. It is shown that the Newton-Wigner position operator, being in this description a constant of motion, acts on states in the augmented space. States with strictly positive energy are non-local in time; consequently, position measurements receive contributions from states representing the particle's position at many times. Apparent superluminal propagation is explained by noting that, as the particle is potentially in the past (or future) of the assumed initial place and time of localization, it has time to propagate to distant regions without exceeding the speed of light. An inequality is proven showing the Hegerfeldt paradox to be completely accounted for by the hypotheses of subluminal propagation from a set of initial space-time points determined by the quantum time distribution arising from the positivity of the system's energy. Spatial localization can nevertheless occur through quantum interference between states representing the particle at different times. The non-locality of the same system to a moving observer is due to Lorentz rotation of spatial axes out of the interference minimum.Comment: This paper is identical to the version appearing in J. Math. Phys. 41; 6093 (Sept. 2000). The published version will be found at http://ojps.aip.org/jmp/. The paper (40 page PDF file) has been completely revised since the last posting to this archiv

Equilibrium Relativistic Mass Distribution for Indistinguishable Events

A manifestly covariant relativistic statistical mechanics of the system of $N$ indistinguishable events with motion in space-time parametrized by an invariant ``historical time'' $\tau$ is considered. The relativistic mass distribution for such a system is obtained from the equilibrium solution of the generalized relativistic Boltzmann equation by integration over angular and hyperbolic angular variables. All the characteristic averages are calculated. Expressions for the pressure and the density of events are found and the relativistic equation of state is obtained. The Galilean limit is considered; the theory is shown to pass over to the usual nonrelativistic statistical mechanics of indistinguishable particles.Comment: TAUP-2115-9

Towards a Realistic Equation of State of Strongly Interacting Matter

We consider a relativistic strongly interacting Bose gas. The interaction is manifested in the off-shellness of the equilibrium distribution. The equation of state that we obtain for such a gas has the properties of a realistic equation of state of strongly interacting matter, i.e., at low temperature it agrees with the one suggested by Shuryak for hadronic matter, while at high temperature it represents the equation of state of an ideal ultrarelativistic Stefan-Boltzmann gas, implying a phase transition to an effectively weakly interacting phase.Comment: LaTeX, figures not include