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

Hypercomplex quantum mechanics

The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective geometry of the weakly modular orthocomplemented lattice of propositions may be imbedded in a complex Hilbert space; this is the structure which has traditionally been used. This paper reviews some work which has been devoted to generalizing the target space of this imbedding to Hilbert modules of a more general type. In particular, detailed discussion is given of the simplest generalization of the complex Hilbert space, that of the quaternion Hilbert module.Comment: Plain Tex, 11 page

Generalized Boltzmann Equation in a Manifestly Covariant Relativistic Statistical Mechanics

We consider the relativistic statistical mechanics of an ensemble of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau .$ We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses, to find the approximate dynamical equation for the kinetic state of any nonequilibrium system to the relativistic case, and obtain a manifestly covariant Boltzmann-type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. This equation is then used to prove the $H$-theorem for evolution in $\tau .$ In the equilibrium limit, the covariant forms of the standard statistical mechanical distributions are obtained. We introduce two-body interactions by means of the direct action potential $V(q),$ where $q$ is an invariant distance in the Minkowski space-time. The two-body correlations are taken to have the support in a relative $O( 2,1)$-invariant subregion of the full spacelike region. The expressions for the energy density and pressure are obtained and shown to have the same forms (in terms of an invariant distance parameter) as those of the nonrelativistic theory and to provide the correct nonrelativistic limit

Strategies to Use Nanoparticles to Generate CD4 and CD8 Regulatory T Cells for the Treatment of SLE and Other Autoimmune Diseases

Autoimmune diseases are disorders of immune regulation where the mechanisms responsible for self-tolerance break down and pathologic T cells overcome the protective effects of T regulatory cells (Tregs) that normally control them. The result can be the initiation of chronic inflammatory diseases. Systemic lupus erythematosus (SLE) and other autoimmune diseases are generally treated with pharmacologic or biological agents that have broad suppressive effects. These agents can halt disease progression, yet rarely cure while carrying serious adverse side effects. Recently, nanoparticles have been engineered to correct homeostatic regulatory defects and regenerate therapeutic antigen-specific Tregs. Some approaches have used nanoparticles targeted to antigen presenting cells to switch their support from pathogenic T cells to protective Tregs. Others have used nanoparticles targeted directly to T cells for the induction and expansion of CD4+ and CD8+ Tregs. Some of these T cell targeted nanoparticles have been formulated to act as tolerogenic artificial antigen presenting cells. This article discusses the properties of these various nanoparticle formulations and the strategies to use them in the treatment of autoimmune diseases. The restoration and maintenance of Treg predominance over effector cells should promote long-term autoimmune disease remission and ultimately prevent them in susceptible individuals

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

Schwinger Algebra for Quaternionic Quantum Mechanics

It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states $N \to \infty$.Comment: 20 pages, Plain Te

Approximate resonance states in the semigroup decomposition of resonance evolution

The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.Comment: LaTex 22 pages 3 figure

The EPR experiment in the energy-based stochastic reduction framework

We consider the EPR experiment in the energy-based stochastic reduction framework. A gedanken set up is constructed to model the interaction of the particles with the measurement devices. The evolution of particles' density matrix is analytically derived. We compute the dependence of the disentanglement rate on the parameters of the model, and study the dependence of the outcome probabilities on the noise trajectories. Finally, we argue that these trajectories can be regarded as non-local hidden variables.Comment: 11 pages, 5 figure

Semigroup evolution in Wigner Weisskopf pole approximation with Markovian spectral coupling

We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation (neglecting the background contribution) the evolution of a total system subspace is not an exact semigroup for the multi-channel decay, unless the projectors into eigesntates of the reduced evolution generator $W(z)$ are orthogonal. In this case these projectors must be evaluated at different pole locations $z_\alpha\neq z_\beta$. Since the orthogonality relation does not generally hold at different values of $z$, for example, when there is symmetry breaking, the semigroup evolution is a poor approximation for the multi-channel decay, even for a very weak coupling. Nevertheless, there exists a possibility not only to ensure the orthogonality of the $W(z)$ projectors regardless the number of the poles, but also to simultaneously suppress the effect of the background contribution. This possibility arises when the theory is generalized to take into account interactions with an environment. In this case $W(z)$, and hence its eigenvectors as well, are {\it independent} of $z$, which corresponds to a structure of the coupling to the continuum spectrum associated with the Markovian limit.Comment: 9 pages, 3 figure