On the supersymmetry of the Dirac-Kepler problem plus a Coulomb-type scalar potential in D+1 dimensions and the generalized Lippmann-Johnson operator

We study the Dirac-Kepler problem plus a Coulomb-type scalar potential by generalizing the Lippmann-Johnson operator to D spatial dimensions. From this operator, we construct the supersymmetric generators to obtain the energy spectrum for discrete excited eigenstates and the radial spinor for the SUSY ground stat

Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse

We present an anomaly-free Dirac constraint quantization of the string-inspired dilatonic gravity (the CGHS model) in an open 2-dimensional spacetime. We show that the quantum theory has the same degrees of freedom as the classical theory; namely, all the modes of the scalar field on an auxiliary flat background, supplemented by a single additional variable corresponding to the primordial component of the black hole mass. The functional Heisenberg equations of motion for these dynamical variables and their canonical conjugates are linear, and they have exactly the same form as the corresponding classical equations. A canonical transformation brings us back to the physical geometry and induces its quantization.Comment: 37 pages, LATEX, no figures, submitted to Physical Review

TWO DIMENSIONAL DILATON GRAVITY COUPLED TO AN ABELIAN GAUGE FIELD

The most general two-dimensional dilaton gravity theory coupled to an Abelian gauge field is considered. It is shown that, up to spacetime diffeomorphisms and $U(1)$ gauge transformations, the field equations admit a two-parameter family of distinct, static solutions. For theories with black hole solutions, coordinate invariant expressions are found for the energy, charge, surface gravity, Hawking temperature and entropy of the black holes. The Hawking temperature is proportional to the surface gravity as expected, and both vanish in the case of extremal black holes in the generic theory. A Hamiltonian analysis of the general theory is performed, and a complete set of (global) Dirac physical observables is obtained. The theory is then quantized using the Dirac method in the WKB approximation. A connection between the black hole entropy and the imaginary part of the WKB phase of the Dirac quantum wave functional is found for arbitrary values of the mass and $U(1)$ charge. The imaginary part of the phase vanishes for extremal black holes and for eternal, non-extremal Reissner-Nordstrom black holes.Comment: Minor revisions only. Some references have been added, and some typographical errors correcte

Seven Steps Towards the Classical World

Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard Quantum Mechanics only the wave function or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical limit becomes very simple: when do the Bohmian trajectories look Newtonian?Comment: 16 pages, LaTeX, uses latexsy