118619230
Quantization of the Jackiw-Teitelboim model
We study the phase space structure of the Jackiw-Teitelboim model in its connection variables formulation where the gauge group of the field theory is given by local SL(2,R)[or SU(2) for the Euclidean model], i.e. the de Sitter group in two dimensions. In order to make the connection with two-dimensional gravity explicit, a partial gauge fixing of the de Sitter symmetry can be introduced that reduces it to space-time diffeomorphisms. This can be done in different ways. Having no local physical degrees of freedom, the reduced phase space of the model is finite dimensional. The simplicity of this gauge field theory allows for studying different avenues for quantization, which may use various (partial) gauge fixings. We show that reduction and quantization are noncommuting operations: the representation of basic variables as operators in a Hilbert space depends on the order chosen for the latter. Moreover, a representation that is natural in one case may not even be available in the other leading to inequivalent quantum theories.
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.
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.
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.
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.
119617684
Beta decay studies with the total absorption technique: Past, present and future
Measurements of beta decay reduced transition probabilities are particularly relevant in nuclei far from the stability line. It has been demonstrated that a proper measurement of this quantity requires the use of the total absorption technique, which has become a reliable tool in recent years, thanks to the increased efficiency of the associated spectrometers and the development of new analysis techniques. In this paper, we present a brief history of the past and present use of these detectors and how they might be developed in the future.
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.
124142447
Higher Spin Black Holes
We review some relevant results in the context of higher spin black holes in three-dimensional spacetimes, focusing on their asymptotic behaviour and thermodynamic properties. For simplicity, we mainly discuss the case of gravity nonminimally coupled to spin-three fields, being nonperturbatively described by a Chern–Simons theory of two independent \(\mathit{sl}\left (3, \mathbb{R}\right )\) gauge fields. Since the analysis is particularly transparent in the Hamiltonian formalism, we provide a concise discussion of their basic aspects in this context; and as a warming up exercise, we briefly analyze the asymptotic behaviour of pure gravity, as well as the BTZ black hole and its thermodynamics, exclusively in terms of gauge fields. The discussion is then extended to the case of black holes endowed with higher spin fields, briefly signaling the agreements and discrepancies found through different approaches. We conclude explaining how the puzzles become resolved once the fall off of the fields is precisely specified and extended to include chemical potentials, in a way that it is compatible with the asymptotic symmetries. Hence, the global charges become completely identified in an unambiguous way, so that different sets of asymptotic conditions turn out to contain inequivalent classes of black hole solutions being characterized by a different set of global charges.
16594811
Higher spin gravity in 3D: Black holes, global charges and thermodynamics
Abstract Global charges and thermodynamic properties of three-dimensional higher spin black holes that have been recently found in the literature are revisited. Since these solutions possess a relaxed asymptotically AdS behavior, following the canonical approach, it is shown that the global charges, and in particular the energy, acquire explicit nontrivial contributions given by nonlinear terms in the deviations with respect to the reference background. It is also found that there are cases for which the first law of thermodynamics can be readily worked out in the canonical ensemble, i.e., without work terms associated to the presence of higher spin fields, and remarkably, the semiclassical higher spin black hole entropy is exactly reproduced from Cardy formula.
118550405
Gravitational solitons, hairy black holes and phase transitions in BHT massive gravity
Hairy black holes and gravitational solitons in three dimensions for the new (BHT) massive gravity theory are considered at the special case when there is a unique maximally symmetric solution. Following the Brown-York approach with suitable counterterms, it is shown that the soliton possesses a fixed negative mass which coincides with that of AdS spacetime regardless the value of the integration constant that describes it. The soliton is then regarded as a degenerate ground state labeled by a modulus parameter. The Euclidean action is shown to be finite and independent of modulus and hair parameters for both classes of solutions, reproducing the hairy black hole free energy. Modular invariance implies that the gravitational hair becomes determined by the modulus parameter. Cardy formula is shown to agree with the semiclassical entropy provided the modulus parameter of the ground state is spontaneously fixed, suggesting that the hairy black hole is in a broken phase. Indeed, it is found that the critical temperature Tc = (2πl)−1 characterizes a first order phase transition between the static hairy black hole and the soliton which, due to the existence of gravitational hair, can take place in the semiclassical regime.