46502819
On the regularization of the constraint algebra of quantum gravity in 2 + 1 dimensions with a nonvanishing cosmological constant
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three-dimensional (Riemannian) gravity with a positive cosmological constant (Λ > 0). We show that the usual regularization techniques (successful in the Λ = 0 case and widely applied in four-dimensional LQG) led to a deformation of the classical constraint algebra (or anomaly) proportional to the local strength of the curvature squared. We argue that this is an unavoidable consequence of the nonlocal nature of generalized connections.
202708693
Characteristic Formulation of the Eikonal Equation
A method of solving the eikonal equation, in either flat or curved spacetimes, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and characteristic data for the same solution, namely they are related by a Legendre transformation. From the resulting solutions, we study and describe their associated wave-front singularities.
18617564
Iterative approach to gravitational lensing theory
We develop an iterative approach to gravitational lensing theory based on approximate solutions of the null geodesic equations. The approach can be employed in any space-time which is ``close'' to a space-time in which the null geodesic equations can be completely integrated, such as Minkowski space-time, Robertson-Walker cosmologies, or Schwarzschild-Kerr geometries. To illustrate the method, we construct the iterative gravitational lens equations and time of arrival equation for a single Schwarzschild lens. This example motivates a discussion of the relationship between the iterative approach, the standard thin lens formulation, and an exact formulation of gravitational lensing.
16607831
Multiple-event probability in general-relativistic quantum mechanics. II. A discrete model
We introduce a simple quantum mechanical model in which time and space are discrete and periodic. These features avoid the complications related to continuous-spectrum operators and infinite-norm states. The model provides a tool for discussing the probabilistic interpretation of generally covariant quantum systems, without the confusion generated by spurious infinities. We use the model to illustrate the formalism of general-relativistic quantum mechanics, and to test the definition of multiple-event probability introduced in a companion paper [Phys. Rev. D 75, 084033 (2007)]. We consider a version of the model with unitary time evolution and a version without unitary time evolution.
14983134
Spin foam diagrammatics and topological invariance
We provide a simple proof of the topological invariance of the Turaev–Viro model (corresponding to simplicial 3D pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF theories. Moreover, we prove the invariance under more general conditions allowing the state sum to be defined on arbitrary cellular decompositions of the underlying manifold. Invariance is governed by a set of identities corresponding to local gluing and rearrangement of cells in the complex. Due to the fully algebraic nature of these identities our results extend to a vast class of quantum groups. The techniques introduced here could be relevant for investigating the scaling properties of non-topological state sums, proposed as models of quantum gravity in 4D, under refinement of the cellular decomposition.
732756
On the quantum origin of the seeds of cosmic structure
The current understanding of the quantum origin of cosmic structure is discussed critically. We point out that in the existing treatments a transition from a symmetric quantum state to an (essentially classical) non-symmetric state is implicitly assumed, but not specified or analysed in any detail. In facing this issue, we are led to conclude that new physics is required to explain the apparent predictive power of the usual schemes. Furthermore, we show that the novel way of looking at the relevant issues opens new windows from where relevant information might be extracted regarding cosmological issues and perhaps even clues about aspects of quantum gravity.
16895941
Relativistic direct Urca processes in cooling neutron stars
Abstract We derive a relativistic expression for neutrino energy losses caused by the direct Urca processes in degenerate baryon matter of neutron stars. We use two different ways to calculate the emissivity caused by the reactions to our interest. First we perform a standard calculation by Fermi's “golden” rule. The second calculation, resulting in the same expression, is performed with the aid of polarization functions of the medium. Our result for neutrino energy losses strongly differs from previous nonrelativistic results. We also discuss nonconservation of the baryon vector current in reactions through weak charged currents in the medium, when the asymmetry between protons and neutrons is considered. The above effects, not discussed in the literature before, substantially modify the polarization functions responsible for the induced weak charged currents in baryon matter.
119114072
Superselection rule for the cosmological constant in three-dimensional spacetime
Efforts to understand the origin of the cosmological constant {\Lambda} and its observed value have led to consider it as a dynamical field rather than as a universal constant. Then the possibility arises that the universe, or regions of it, might be in a superposition of quantum states with different values of {\Lambda}, so that its actual value would not be definite. There appears to be no argument to rule out this possibility for a generic spacetime dimension D. However, as proved herein, for D=3 there exists a superselection rule that forbids such superpositions. The proof is based on the asymptotic symmetry algebra.
11750374
On relativistic approaches to the pion self-energy in nuclear matter
Abstract.We argue that, in contrast to the non-relativistic approach, a relativistic evaluation of the nucleon-hole and delta-isobar-nucleon-hole contributions to the pion self-energy incorporates the s-wave scattering, whose magnitude within the RPA is in conflict with the near-threshold behavior imposed by chiral symmetry. As a result, a relativistic approach to the pion self-energy in isospin-symmetric nuclear matter, containing only these diagrams, does not satisfy the known experimental results on the near-threshold behavior of the $\pi$-nucleon (forward) scattering amplitude.
17920276
Relativistic short-range correlation effects on the pion dynamics in nuclear matter
Replicated theoretical attempts of relativistic approaches to the pion self-energy in nuclear matter yield unphysical pion spectra. We demonstrate the crucial dependence of the calculated pion spectra on the correct relativistic accounting for the short-range correlation effects on the pion self-energy in the medium. To do this, we simulate the short-range interactions by phenomenological contact terms in the relativistic Lagrangian density, and derive the pion self-energy by carefully taking into account the relativistic kinematics. The obtained spectrum for the pion-like excitations in cold nuclear matter shows physically meaningful branches, in contrast to those obtained before by different authors by the use of simplified relativistic approaches to the short-range correlations.
122905847
Topological gravity from a transgression gauge field theory
Abstract It is shown that a topological action for gravity in even dimensions can be obtained from a gravity theory whose Lagrangian is given by a transgression form invariant under the Poincare group. The field ϕ a , which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associated with the non-linear realizations of the Poincare group ISO ( d − 1 , 1 ) .