Quantum Mechanics in Non-Inertial Frames with a Multi-Temporal Quantization Scheme: II) Non-Relativistic Particles

The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid non-inertial frames, containing the standard rigidly linear accelereted and rotating ones, is given in the framework of parametrized Galilei theories. Then the multi-temporal quantization, in which the gauge variables, describing the non-inertial effects, are not quantized but considered as c-number generalized times, is applied to non relativistic particles. It is shown that with a suitable ordering there is unitary evolution in all times and that, after the separation of center of mass, it is still possible to identify the inertial bound states. The few existing results of quantization in rigid non-inertial frames are recovered as special cases

General features of Bianchi-I cosmological models in Lovelock gravity

We derived equations of motion corresponding to Bianchi-I cosmological models in the Lovelock gravity. Equations derived in the general case, without any specific ansatz for any number of spatial dimensions and any order of the Lovelock correction. We also analyzed the equations of motion solely taking into account the highest-order correction and described the drastic difference between the cases with odd and even numbers of spatial dimensions. For power-law ansatz we derived conditions for Kasner and generalized Milne regimes for the model considered. Finally, we discuss the possible influence of matter in the form of perfect fluid on the solutions obtained.Comment: extended version of published Brief Repor

The relation between the model of a crystal with defects and Plebanski's theory of gravity

In the present investigation we show that there exists a close analogy of geometry of spacetime in GR with a structure of defects in a crystal. We present the relation between the Kleinert's model of a crystal with defects and Plebanski's theory of gravity. We have considered the translational defects - dislocations, and the rotational defects - disclinations - in the 3- and 4-dimensional crystals. The 4-dimensional crystalline defects present the Riemann-Cartan spacetime which has an additional geometric property - "torsion" - connected with dislocations. The world crystal is a model for the gravitation which has a new type of gauge symmetry: the Einstein's gravitation has a zero torsion as a special gauge, while a zero connection is another equivalent gauge with nonzero torsion which corresponds to the Einstein's theory of "teleparallelism". Any intermediate choice of the gauge with nonzero connection A^{IJ}_\mu is also allowed. In the present investigation we show that in the Plebanski formulation the phase of gravity with torsion is equivalent to the ordinary or topological gravity, and we can exclude a torsion as a separate dynamical variable.Comment: 13 pages, 2 figure

On the extension of the concept of Thin Shells to The Einstein-Cartan Theory

This paper develops a theory of thin shells within the context of the Einstein-Cartan theory by extending the known formalism of general relativity. In order to perform such an extension, we require the general non symmetric stress-energy tensor to be conserved leading, as Cartan pointed out himself, to a strong constraint relating curvature and torsion of spacetime. When we restrict ourselves to the class of space-times satisfying this constraint, we are able to properly describe thin shells and derive the general expression of surface stress-energy tensor both in its four-dimensional and in its three-dimensional intrinsic form. We finally derive a general family of static solutions of the Einstein-Cartan theory exhibiting a natural family of null hypersurfaces and use it to apply our formalism to the construction of a null shell of matter.Comment: Latex, 21 pages, 1 combined Latex/Postscript figure; Accepted for publication in Classical and Quantum Gravit

Matrix Gravity and Massive Colored Gravitons

We formulate a theory of gravity with a matrix-valued complex vierbein based on the SL(2N,C)xSL(2N,C) gauge symmetry. The theory is metric independent, and before symmetry breaking all fields are massless. The symmetry is broken spontaneously and all gravitons corresponding to the broken generators acquire masses. If the symmetry is broken to SL(2,C) then the spectrum would correspond to one massless graviton coupled to $2N^2 -1$ massive gravitons. A novel feature is the way the fields corresponding to non-compact generators acquire kinetic energies with correct signs. Equally surprising is the way Yang-Mills gauge fields acquire their correct kinetic energies through the coupling to the non-dynamical antisymmetric components of the vierbeins.Comment: One reference adde

Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter

Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion configurations with a localized, conserved charge that adopts integer values. The charge is topological in nature and the torsional configurations can be thought of as torsional `monopole' solutions. We explore some of the properties of these configurations in gravity models with non-vanishing curvature, and discuss the possible existence of such monopoles in condensed matter systems. To conclude, we show how the monopoles can be thought of as a natural generalization of the Cartan spiral staircase.Comment: 4+epsilon, 1 figur

Decoherence of an nn-qubit quantum memory

We analyze decoherence of a quantum register in the absence of non-local operations i.e. of $n$ non-interacting qubits coupled to an environment. The problem is solved in terms of a sum rule which implies linear scaling in the number of qubits. Each term involves a single qubit and its entanglement with the remaining ones. Two conditions are essential: first decoherence must be small and second the coupling of different qubits must be uncorrelated in the interaction picture. We apply the result to a random matrix model, and illustrate its reach considering a GHZ state coupled to a spin bath.Comment: 4 pages, 2 figure

Post-Newtonian extension of the Newton-Cartan theory

The theory obtained as a singular limit of General Relativity, if the reciprocal velocity of light is assumed to tend to zero, is known to be not exactly the Newton-Cartan theory, but a slight extension of this theory. It involves not only a Coriolis force field, which is natural in this theory (although not original Newtonian), but also a scalar field which governs the relation between Newtons time and relativistic proper time. Both fields are or can be reduced to harmonic functions, and must therefore be constants, if suitable global conditions are imposed. We assume this reduction of Newton-Cartan to Newton`s original theory as starting point and ask for a consistent post-Newtonian extension and for possible differences to usual post-Minkowskian approximation methods, as developed, for example, by Chandrasekhar. It is shown, that both post-Newtonian frameworks are formally equivalent, as far as the field equations and the equations of motion for a hydrodynamical fluid are concerned.Comment: 13 pages, LaTex, to appear in Class. Quantum Gra

Null Killing Vector Dimensional Reduction and Galilean Geometrodynamics

The solutions of Einstein's equations admitting one non-null Killing vector field are best studied with the projection formalism of Geroch. When the Killing vector is lightlike, the projection onto the orbit space still exists and one expects a covariant theory with degenerate contravariant metric to appear, its geometry is presented here. Despite the complications of indecomposable representations of the local Euclidean subgroup, one obtains an absolute time and a canonical, Galilean and so-called Newtonian, torsionless connection. The quasi-Maxwell field (Kaluza Klein one-form) that appears in the dimensional reduction is a non-separable part of this affine connection, in contrast to the reduction with a non-null Killing vector. One may define the Kaluza Klein scalar (dilaton) together with the absolute time coordinate after having imposed one of the equations of motion in order to prevent the emergence of torsion. We present a detailed analysis of the dimensional reduction using moving frames, we derive the complete equations of motion and propose an action whose variation gives rise to all but one of them. Hidden symmetries are shown to act on the space of solutions.Comment: LATEX, 41 pages, no figure

Torsion, an alternative to dark matter?

We confront Einstein-Cartan's theory with the Hubble diagram. An affirmative answer to the question in the title is compatible with today's supernovae data.Comment: 14 pp, 3 figures. Version 2 matches the version published in Gen. Rel. Grav., references added. Version 3 corrects a factor 3 in Cartan's equations to become