Semiclassical scalar propagators in curved backgrounds: formalism and ambiguities

The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing --often at the gedankenexperiment level-- constraints on tentative theories of quantum gravity. Determining the dynamics of fields in curved backgrounds remains however a complicated task because of the highly intricate partial differential equations involved, especially when the space metric exhibits no symmetry. In this article, we provide --in a pedagogical way-- a general formalism to determine this dynamics at the semiclassical order. To this purpose, a generic expression for the semiclassical propagator is computed and the equation of motion for the probability four-current is derived. Those results underline a direct analogy between the computation of the propagator in general relativistic quantum mechanics and the computation of the propagator for stationary systems in non-relativistic quantum mechanics. A possible application of this formalism to curvature-induced quantum interferences is also discussed.Comment: New materials on gravitationally-induced quantum interferences has been adde

Lorentz Symmetry Breaking in Abelian Vector-Field Models with Wess-Zumino Interaction

We consider the abelian vector-field models in the presence of the Wess-Zumino interaction with the pseudoscalar matter. The occurence of the dynamic breaking of Lorentz symmetry at classical and one-loop level is described for massless and massive vector fields. This phenomenon appears to be the non-perturbative counterpart of the perturbative renormalizability and/or unitarity breaking in the chiral gauge theories.Comment: 11 pages,LaTeX, Preprint DFUB/94 - 1

Spinor two-point functions and Peierls bracket in de Sitter space

This paper studies spinor two-point functions for spin-1/2 and spin-3/2 fields in maximally symmetric spaces such as de Sitter spacetime, by using intrinsic geometric objects. The Feynman, positive- and negative-frequency Green functions are then obtained for these cases, from which we eventually display the supercommutator and the Peierls bracket under such a setting in two-component-spinor language.Comment: 22 pages, Latex. In the final version, the presentation has been improve

Coupling of Linearized Gravity to Nonrelativistic Test Particles: Dynamics in the General Laboratory Frame

The coupling of gravity to matter is explored in the linearized gravity limit. The usual derivation of gravity-matter couplings within the quantum-field-theoretic framework is reviewed. A number of inconsistencies between this derivation of the couplings, and the known results of tidal effects on test particles according to classical general relativity are pointed out. As a step towards resolving these inconsistencies, a General Laboratory Frame fixed on the worldline of an observer is constructed. In this frame, the dynamics of nonrelativistic test particles in the linearized gravity limit is studied, and their Hamiltonian dynamics is derived. It is shown that for stationary metrics this Hamiltonian reduces to the usual Hamiltonian for nonrelativistic particles undergoing geodesic motion. For nonstationary metrics with long-wavelength gravitational waves (GWs) present, it reduces to the Hamiltonian for a nonrelativistic particle undergoing geodesic \textit{deviation} motion. Arbitrary-wavelength GWs couple to the test particle through a vector-potential-like field $N_a$, the net result of the tidal forces that the GW induces in the system, namely, a local velocity field on the system induced by tidal effects as seen by an observer in the general laboratory frame. Effective electric and magnetic fields, which are related to the electric and magnetic parts of the Weyl tensor, are constructed from $N_a$ that obey equations of the same form as Maxwell's equations . A gedankin gravitational Aharonov-Bohm-type experiment using $N_a$ to measure the interference of quantum test particles is presented.Comment: 38 pages, 7 figures, written in ReVTeX. To appear in Physical Review D. Galley proofs corrections adde

Quantum Effects in the Spacetime of a Magnetic Flux Cosmic String

In this work we compute the vacuum expectation values of the energy-momentum tensor and the average value of a massive, charged scalar field in the presence of a magnetic flux cosmic string for both zero- and finite-temperature cases.Comment: To appear in the Int. Journal of Modern Phys. A (special issue). Proceedings of the Second International Londrina Winter School on Mathematical Methods in Physics, Londrina, Brazil, August 200

Gaseous-Hydrogen Pressurant Requirements for the Discharge of Liquid Hydrogen from a 3.96 Meter /13 ft/ Diameter Spherical Tank

Hydrogen gas pressure requirements during pressurization and transfer of liquid hydrogen from spherical tank

Yang-Mills action from minimally coupled bosons on R^4 and on the 4D Moyal plane

We consider bosons on Euclidean R^4 that are minimally coupled to an external Yang-Mills field. We compute the logarithmically divergent part of the cut-off regularized quantum effective action of this system. We confirm the known result that this term is proportional to the Yang-Mills action. We use pseudodifferential operator methods throughout to prepare the ground for a generalization of our calculation to the noncommutative four-dimensional Moyal plane (also known as noncommutative flat space). We also include a detailed comparison of our cut-off regularization to heat kernel techniques. In the case of the noncommutative space, we complement the usual technique of asymptotic expansion in the momentum variable with operator theoretic arguments in order to keep separated quantum from noncommutativity effects. We show that the result from the commutative space R^4 still holds if one replaces all pointwise products by the noncommutative Moyal product.Comment: 37 pages, v2 contains an improved treatment of the theta function in Appendix A.

Graded Majorana spinors

In many mathematical and physical contexts spinors are treated as Grassmann odd valued fields. We show that it is possible to extend the classification of reality conditions on such spinors by a new type of Majorana condition. In order to define this graded Majorana condition we make use of pseudo-conjugation, a rather unfamiliar extension of complex conjugation to supernumbers. Like the symplectic Majorana condition, the graded Majorana condition may be imposed, for example, in spacetimes in which the standard Majorana condition is inconsistent. However, in contrast to the symplectic condition, which requires duplicating the number of spinor fields, the graded condition can be imposed on a single Dirac spinor. We illustrate how graded Majorana spinors can be applied to supersymmetry by constructing a globally supersymmetric field theory in three-dimensional Euclidean space, an example of a spacetime where standard Majorana spinors do not exist.Comment: 16 pages, version to appear in J. Phys. A; AFK previously published under the name A. F. Schunc

Noncommutative Complex Scalar Field and Casimir Effect

A noncommutative complex scalar field, satisfying the deformed canonical commutation relations proposed by Carmona et al. [27]-[31], is constructed. Using these noncommutative deformed canonical commutation relations, a model describing the dynamics of the noncommutative complex scalar field is proposed. The noncommutative field equations are solved, and the vacuum energy is calculated to the second order in the parameter of noncommutativity. As an application to this model, the Casimir effect, due to the zero point fluctuations of the noncommutative complex scalar field, is considered. It turns out that in spite of its smallness, the noncommutativity gives rise to a repulsive force at the microscopic level, leading to a modifed Casimr potential with a minimum at the point amin= racine(5/84){\pi}{\theta}.Comment: Revtex style, 28 page

A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter

We consider stationary, axially and equatorially symmetric systems consisting of a central rotating and charged degenerate black hole and surrounding matter. We show that $a^2+Q^2=M^2$ always holds provided that a continuous sequence of spacetimes can be identified, leading from the Kerr-Newman solution in electrovacuum to the solution in question. The quantity $a=J/M$ is the black hole's intrinsic angular momentum per unit mass, $Q$ its electric charge and $M$ the well known black hole mass parameter introduced by Christodoulou and Ruffini.Comment: 19 pages, 2 figures, replaced with published versio