Quantum spacetime

After a review and reformulation of previous results, further developments in the construction and interpretation of a quantum-theoretic model of general relativistic spacetime are presented. A theorem is proved that clarifies the nature of the boundaries separating the four-dimensional facets of the resulting piecewise linear model, and a simple example of such a spacetime is detailed. The precise way in which any such model unifies the essential features of both quantum theory and general relativity is discussed.     

Gauged supergravities in various spacetime dimensions

In this review article we study the gaugings of extended supergravity theories in various space‐time dimensions. These theories describe the low‐energy limit of non‐trivial string compactifications. For each theory under consideration we review all possible gaugings that are compatible with supersymmetry. They are parameterized by the so‐called embedding tensor which is a group theoretical object that has to satisfy certain representation constraints. This embedding tensor determines all couplings in the gauged theory that are necessary to preserve gauge invariance and supersymmetry. The concept of the embedding tensor and the general structure of the gauged supergravities are explained in detail. The methods are then applied to the half‐maximal (N = 4) supergravities in d = 4 and d = 5 and to the maximal supergravities in d = 2 and d = 7. Examples of particular gaugings are given. Whenever possible, the higher‐dimensional origin of these theories is identified and it is shown how the compactification parameters like fluxes and torsion are contained in the embedding tensor.     

Quantum electrodynamics on noncommutative spacetime

We propose a new method to quantize gauge theories formulated on a canonical noncommutative spacetime with fields and gauge transformations taken in the enveloping algebra. We show that the theory is renormalizable at one loop and compute the beta function and show that the spin dependent contribution to the anomalous magnetic moment of the fermion at one loop has the same value as in the commutative quantum electrodynamics case.     

Quantum teleportation and Kerr-Newman spacetime

We consider the teleportation in the background of Kerr-Newman spacetime. Because of the Hawking effect, the fidelity of the teleportation is reduced. The results also show the fidelity is closely related to the mass, charge and rotating velocity of the black hole: high fidelity can be reached for massive, slowly rotating Kerr-Newman black holes.     

Quantum construction of general relativistic spacetime

A construction of a model of general relativistic spacetime that arises naturally from within standard quantum theory is presented. In terms of this model all the usual structures of general relativity theory can be given a quantum-theoretic interpretation, so that the usual barriers between the two theories are absent.     

Quantum theoretical origin of spacetime structure

The possibility that macroscopic spacetime is defined by the observable structure of the simplest nontrivial quantum systems is investigated.     

Quantum field-theory models on fractal spacetime

Continuing the analysis of a previous paper, the present work applies rigorous renormalization group methods to the hierarchical models to establish the existence of field theories with non-Gaussian ultraviolet renormalization group fixed points in 4- dimensions.     

Quantum field theory in curved spacetime

Quantum field theory predicts a number of unusual physical effects in non-Minkowskian manifolds (flat or curved) that have no immediate analogs in Minkowski spacetime. The following examples are reviewed: (1) The Casimir effect; (2) Radiation from accelerating conductors; (3) Particle production in manifolds with horizons, including both stationary black holes and black holes formed by collapse. In the latter examples curvature couples directly to matter through the stress tensor and induces the creation of real particles. However, it also induces serious divergences in the vacuum stress. These divergences are analyzed, and methods for handling them are reviewed.     

Quantum field-theory models on fractal spacetime

The present work explores the possibility of giving a non-perturbative definition of the quantum field-theory models in non-integer dimensions, which have been previously studied by Wilson and others using analytic continuation of dimension in perturbation integrals. The method employed here is to base the models on fractal point-sets of non-integer Hausdorff-Besicovitch dimension. Two types of scalar-field models are considered: the one has its propagator (=covariance operator kernel) given by a proper-time or heat-kernel representation and the other has a hierarchical propagator. The fractal lattice version of the proper-time propagator is shown to be reflection-positive. The hierarchical models are introduced and their properties discussed on an informal basis.This paper is based largely on the thesis presented by the author for the degree doctor of philosophy in physics at the Ohio State University in 1987     

Quantum dots in graphene

We suggest a way of confining quasiparticles by an external potential in a small region of a graphene strip. Transversal electron motion plays a crucial role in this confinement. Properties of thus obtained graphene quantum dots are investigated theoretically for different types of the boundary conditions at the edges of the strip. The (quasi)bound states exist in all systems considered. At the same time, the dependence of the conductance on the gate voltage carries information about the shape of the edges.     

Quantum matrices inN dimensions

We obtain the commutation relation between rows and columns ofN ×N quantum matrices. We derive the quantum determinant and discuss its property in terms of the q-deformed Levi-Civita symbol. We find the inverse and trace ofN×N quantum matrices. Finally we discuss the q-deformed complexification of the quantum matrices.     

Charged black holes and additional dimensions

A multidimensional generalization is obtained for the Reissner-Nordstrom solution of general relativity theory for the case of n Ricci-plane internal spaces with inclusion of the dilaton field. A two-parameter family of solutions that describe black holes of arbitrary dimensionality D is identified. It is shown that nontrivial black holes with dimensionality D > 4 exist only for nonzero electric charge. The observational consequences, particularly a violation of Coulomb's law, are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 24–28, July, 1991.     

Quantum fluctuations of vacuum stress tensors and spacetime curvatures

We analyze the quantum fluctuations of vacuum stress tensors and spacetime curvatures, using the framework of linear response theory which connects these fluctuations to dissipation mechanisms arising when stress tensors and spacetime metric are coupled. Vacuum fluctuations of spacetime curvatures are shown to be a sum of two contributions at lowest orders; the first one corresponds to vacuum gravitational waves and is restricted to light-like wavevectors and vanishing Einstein curvature, while the second one arises from gravity of vacuum stress tensors. From these fluctuations, we deduce noise spectra for geodesic deviations registered by probe fields which determine ultimate limits in length or time measurements. In particular, a relation between noise spectra characterizing spacetime fluctuations and the number of massless neutrino fields is obtained.