Quantum noncommutative multidimensional cosmology

We present exact quantum solutions for a noncommutative, multidimensional cosmological model and show that stabilization of extra dimensions sets in with the introduction of noncommutativity between the scale factors. An interpretation is offered to accommodate the notion of time, rendering comparison with the classical solutions possible.     

Quantum diffusions and the noncommutative torus

Quantum diffusions driven by the creation and annihilation processes on the noncommutative torus algebra are considered. A cohomological obstruction to the existence of such a diffusion is overcome by constructing a diffusion on a larger algebra. There are implications for models in solid-state physics based on the noncommutative torus.     

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 Hall effect in noncommutative quantum mechanics

We study the quantum Hall (QH) effect for an electron moving in a plane whose coordinates and momenta are noncommuting under the influence of uniform external magnetic and electric fields. After solving the time independent Schrödinger equation both on a noncommutative space (NCS) and a noncommutative phase space (NCPS), we obtain the energy eigenvalues and eigenfunctions of the relevant Hamiltonian. We derive the electric current whose expectation value gives the QH effect both on a NCS and a NCPS.     

Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes

In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel’d twists. We construct deformed quadratic action functionals and compute the corresponding equation of motion operators. The Green’s operators and the fundamental solution of the deformed equation of motion are obtained in terms of formal power series. It is shown that, using the deformed fundamental solution, we can define deformed *-algebras of field observables, which in general depend on the spacetime deformation parameter. This dependence is absent in the special case of Killing deformations, which include in particular the Moyal-Weyl deformation of the Minkowski spacetime.     

Quantum field theory in black hole-type spacetimes with horizons

Using quantum field theory in black hole-type spacetimes with horizons, which includes all the black hole solutions and also some other interesting solutions in general relativity, we obtain Hawking's thermal spectrum of Dirac particles near the event horizon as well as the cosmological horizon of the spacetime.     

Quantum gravity,field theory and signatures of noncommutative spacetime

A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what extent noncommutative gauge theories may be regarded as gauge theories of gravity. UV/IR mixing is explained in detail and we describe its relations to renormalization, to gravitational dynamics, and to deformed dispersion relations in models of quantum spacetime of interest in string theory and in doubly special relativity. We also discuss some potential experimental probes of spacetime noncommutativity.     

Quantum mechanics on noncommutative plane and sphere from constrained systems

It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints presented in the models. It leads, in particular, to a possibility of quantization in terms of the initial NC variables. For a two-dimensional plane we present two Lagrangian actions, one of which admits addition of an arbitrary potential. Quantization leads to quantum mechanics with ordinary product replaced by the Moyal product. For a three-dimensional case we present Lagrangian formulations for a particle on NC sphere as well as for a particle on commutative sphere with a magnetic monopole at the center, the latter is shown to be equivalent to the model of usual rotor. There are several natural possibilities to choose physical variables, which lead either to commutative or to NC brackets for space variables. In the NC representation all information on the space variable dynamics is encoded in the NC geometry. Potential of special form can be added, which leads to an example of quantum mechanics on the NC sphere.     

Gravitational geons on the brane

In this paper, we examine the possibility of static, spherically symmetric gravitational geons on a 3 dimensional brane embedded in a 4+1 dimensional space-time. We choose a specific g _tt for the brane-world space-time metric. We then calculate g _rr analytically in the weak field limit and numerically for stronger fields. We show that the induced field equations on the brane do admit gravitational geon solutions.     

Quantum correction to the entropy of noncommutative BTZ black hole

In this paper we consider the generalized uncertainty principle (GUP) in the tunneling formalism via Hamilton–Jacobi method to determine the quantum-corrected Hawking temperature and entropy for noncommutative BTZ black hole. In our results we obtain several types of corrections including the expected logarithmic correction to the area entropy associated with the noncommutative BTZ black holes. We also show that the area entropy product of the noncommutative BTZ black holes is dependent on mass and by analyzing the nature of the specific heat capacity we have observed that the noncommutative BTZ black hole is stable at some range of parameters.     

Some properties of topological geons

We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g ₀). We use relations between different Lorentzian structures unequivalent tog ₀ and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog ₀ by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e.     

Quantum gravity boundary terms from the spectral action of noncommutative space

We study the boundary terms of the spectral action of the noncommutative space, defined by the spectral triple dictated by the physical spectrum of the standard model, unifying gravity with all other fundamental interactions. We prove that the spectral action predicts uniquely the gravitational boundary term required for consistency of quantum gravity with the correct sign and coefficient. This is a remarkable result given the lack of freedom in the spectral action to tune this term.     

Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels

We have studied a quantum dot with Rashba spin-orbit interaction in noncommutative phase space. The energy eigenvalues are analogous to Landau energy levels. It is shown that this system is related with a physically realizable model of a quantum dot with Rashba spin-orbit interaction in a magnetic field whereby a relation is derived among the noncommutative parameters, spin-orbit coupling strength and magnetic field.     

Internal symmetry groups of quantum geons

In canonical quantum gravity asymptotically trivial diffeomorphisms not deformable to the identity can act nontrivially on the quantum state space. We show that for many 3-manifolds, the inequivalent diffeomorphisms comprise coverings in SU(2) of crystallographic groups. When the diffeomorphism R_2π associated with 2π-rotation is nontrivial, state vectors can have half-integral angular momentum; we list all 3-manifolds with R_2π trivial.     

Bi-metric pseudo-Finslerian spacetimes

Finsler spacetimes have become increasingly popular within the theoretical physics community over the last two decades. However, because physicists need to use pseudo-Finsler structures to describe propagation of signals, there will be nonzero null vectors in both the tangent and cotangent spaces — this causes significant problems in that many of the mathematical results normally obtained for “usual” (Euclidean signature) Finsler structures either do not apply, or require significant modifications to their formulation and/or proof. We shall first provide a few basic definitions, explicitly demonstrating the interpretation of bi-metric theories in terms of pseudo-Finsler norms. We shall then discuss the tricky issues that arise when trying to construct an appropriate pseudo-Finsler metric appropriate to bi-metric spacetimes. Whereas in Euclidian signature the construction of the Finsler metric typically fails only at the zero vector, in Lorentzian signature the Finsler metric is typically ill-defined on the entire null cone. Consequently it is not a good idea to try to encode bi-metricity into pseudo-Finsler geometry. One has to be very careful when applying the concept of pseudo-Finsler geometry in physics.     

On singularity-free spacetimes

We consider here the metric for the singularity-free family of fluid models. The metric is unique for cylindrically symmetric space-time with metric potentials being separable functions of radial and time coordinates in the comoving coordinates. It turns out that fluid models separate out into two classes, withρ ≠μp in general butρ = 3p in particular andp =ρ. It is shown that in both the cases radial heat flow can be incorporated without disturbing the singularity-free character of the spacetime. The geodesics of the singularity-free metric are studied and the geodesic completeness is established. Several previously known solutions are derived as particular cases.