Solutions of Quantum Gravity Coupled to the Scalar Field

We consider the Wheeler-De Witt equation for canonical quantum gravity coupled to massless scalar field. After regularizing and renormalizing this equation, we find a one-parameter class of its solutions.Comment: 8 pages, LaTe

Black Hole Solution of Quantum Gravity

We present a spherically symmetric and static exact solution of Quantum Einstein Equations. This solution is asymptotically (for large $r$) identical with the black hole solution on the anti--De Sitter background and, for some range of values of the mass possesses two horizons. We investigate thermodynamical properties of this solution.Comment: Plain Latex, 10 page

Ballistic transport: A view from the quantum theory of motion

Ballistic transport of electrons through a quantum wire with a constriction is studied in terms of Bohm's interpretation of quantum mechanics, in which the concept of a particle orbit is permitted. The classical bouncing ball trajectories, which justify the name ``ballistic transport'', are established in the large wave number limit. The formation and the vital role of quantum vortices is investigated.Comment: 14 pages, revtex, 4 postscript figure

Complex Energies and Beginnings of Time Suggest a Theory of Scattering and Decay

Many useful concepts for a quantum theory of scattering and decay (like Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially decaying Gamow vectors, causality) are not well defined in the mathematical frame set by the conventional (Hilbert space) axioms of quantum mechanics. Using the Lippmann-Schwinger equations as the takeoff point and aiming for a theory that unites resonances and decay, we conjecture a new axiom for quantum mechanics that distinguishes mathematically between prepared states and detected observables. Suggested by the two signs $\pm i\epsilon$ of the Lippmann-Schwinger equations, this axiom replaces the one Hilbert space of conventional quantum mechanics by two Hardy spaces. The new Hardy space theory automatically provides Gamow kets with exponential time evolution derived from the complex poles of the $S$-matrix. It solves the causality problem since it results in a semigroup evolution. But this semigroup brings into quantum physics a new concept of the semigroup time $t=0$, a beginning of time. Its interpretation and observations are discussed in the last section.Comment: 27 pages, 3 figure

Topological Aspects of the Non-adiabatic Berry Phase

The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a critical frequency. The first Chern number that classifies these bundles is proportional to angular momentum. The non-adiabatic principal bundle over the parameter space is not well-defined at the critical frequency.Comment: 14 pages, Dep. of Physics, Uni. of Texas at Austin, Austin, Texas 78712, to appear in J. Physics

Quantal Time Asymmetry: Mathematical Foundation And Physical Interpretation

Time in standard quantum mechanics extends from -infinity -infinity since according to causality, a quantum state phi(+) must be prepared first at a particular time t = t(0), before the probability vertical bar(psi(-)(t),phi+(t(0))vertical bar(2) for an observable psi(-) can be measured in it at t > t(0) (Feynman (1948)). In experiments on single Ba(+) ions, Dehmelt and others observed this finite preparation time as the ensemble of onset-times t(0)(1),t(0)(2), ..., t(0)(n) of dark periods. How the semigroup time evolution, t(0) equivalent to 0 < t < infinity with a beginning of time t(0), can suggest the parametrization of the resonance pole position of the Z-boson at S= s(R) as s(R) = (M(R) - i Gamma(R)/2)(2) in terms of a mass M(R) and a width Gamma(R) given by a lifetime tau = (h) over bar/Gamma(R), is the subject of this contribution dedicated to Augusto Garcia.Physic

BAANKRUPTCY-Usury-Plaintiff\u27s Claim for Compound Interest Ruled Usurious; Simple Interest Disallowed to Give Effect to State\u27s Deterrence Policy

Usury is the charging of interest for the use of money as a rate in excess of that permitted by statute. The Bankruptcy Act allows the trustee-in-bankruptcy to plead the defense of usury to a creditor\u27s claim. A debtor-in-possession in a Chapter XI proceeding, who has all the rights and powers of the trustee, may also assert the defense of usury. There is, however, no federal usury statute and the Bankruptcy Act defines neither usury nor its effect. To resolve the usury issue the bankruptcy court has to look to the law of the jurisdiction in which the loan arose. The conflict among the state jurisdictions as to the effect given to an usurious loan obscures bankruptcy\u27s traditional distinction between the allowance and the enforcement of a claim. Relying on an unconstrued and unenforced criminal usury statute to invoke local deterrence policy, the court deprived a good faith lender of the proper determination of his ratable share in the bankruptcy distribution

Clebsch-Gordan Coefficients for the Extended Quantum-Mechanical Poincar\'e Group and Angular Correlations of Decay Products

This paper describes Clebsch-Gordan coefficients (CGCs) for unitary irreducible representations (UIRs) of the extended quantum mechanical Poincar\'e group \pt. `Extended' refers to the extension of the 10 parameter Lie group that is the Poincar\'e group by the discrete symmetries $C$, $P$, and $T$; `quantum mechanical' refers to the fact that we consider projective representations of the group. The particular set of CGCs presented here are applicable to the problem of the reduction of the direct product of two massive, unitary irreducible representations (UIRs) of \pt with positive energy to irreducible components. Of the sixteen inequivalent representations of the discrete symmetries, the two standard representations with $U_C U_P = \pm 1$ are considered. Also included in the analysis are additive internal quantum numbers specifying the superselection sector. As an example, these CGCs are applied to the decay process of the $\Upsilon(4S)$ meson.Comment: 26 pages, double spaced. Version 2: typos corrected, introduction change

Topological Black Holes in Quantum Gravity

We derive the black hole solutions with horizons of non-trivial topology and investigate their properties in the framework of an approach to quantum gravity being an extension of Bohm's formulation of quantum mechanics. The solutions we found tend asymptotically (for large $r$) to topological black holes. We also analyze the thermodynamics of these space-times.Comment: 4pages, no figures, plain LaTe

Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group

The velocity basis of the Poincare group is used in the direct product space of two irreducible unitary representations of the Poincare group. The velocity basis with total angular momentum j will be used for the definition of relativistic Gamow vectors.Comment: 14 pages; revte