9066120
Introduction to loop quantum gravity and spin foams
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a starting point in the program, is described in a simple manner. The main ideas leading to the definition of the quantum theory are naturally introduced and the basic mathematics involved is described. The main predictions of the theory such as the discovery of Planck scale discreteness of geometry and the computation of black hole entropy are reviewed. The quantization and solution of the constraints is explained by drawing analogies with simpler systems. Difficulties associated with the quantization of the scalar constraint are discussed.In a second part of the notes, the basic ideas behind the spin foam approach are presented in detail for the simple solvable case of 2+1 gravity. Some results and ideas for four dimensional spin foams are reviewed.
116895326
A Finiteness proof for the Lorentzian state sum spin foam model for quantum general relativity
We show that the normalized Lorentzian state sum is finite on any triangulation. It thus provides a candidate for a perturbatively finite quantum theory of general relativity in four dimensions with Lorentzian signature.
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.
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.
119791906
Comparative studies of lensing methods
Predictions of the standard thin lens approximation and a new iterative approach to gravitational lensing are compared with an ``exact'' approach in simple test cases involving one or two lenses. We show that the thin lens and iterative approaches are remarkably accurate in predicting time delays, source positions and image magnifications for a single monopole lens. However, observationally significant errors were found when the thin lens method was applied to lensing configurations with two lenses. In these cases, the iterative method remained accurate beyond observational limits.
208165775
The spin-foam-representation of LQG
The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity (LQG) is a promising proposal for addressing this difficult task. Despite the steady progress of the field, dynamics remains to a large extend an open issue in LQG. Here we present the main ideas behind a series of proposals for addressing the issue of dynamics. We refer to these constructions as the spin foam representation of LQG. This set of ideas can be viewed as a systematic attempt at the construction of the path integral representation of LQG. The spin foam representation is mathematically precise in 2+1 dimensions, so we will start this chapter by showing how it arises in the canonical quantization of this simple theory. This toy model will be used to precisely describe the true geometric meaning of the histories that are summed over in the path integral of generally covariant theories. In four dimensions similar structures appear. We call these constructions spin foam models as their definition is incomplete in the sence that at least one of the following issues remains unclear: 1) the connection to a canonical formulation, and 2) regularization independence (renormalizability). In the second part of this chapter we will describe the definition of these models emphasizing the importance of these open issues.
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.
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.
44018557
Screening Effects in Relativistic Models of Dense Matter at Finite Temperature
We investigate screening effects of the medium on the potential interaction between two static 'charges' for different models of dense plasmas in the one-boson exchange approximation. The potential can exhibit an oscillatory behavior, which is related to the analytic structure of the corresponding boson propagators in the complex $q$-plane. We have first revisited the one-pion exchange in a nuclear medium. In addition to Friedel oscillations, which are associated to branch cuts in the $q$-plane, there appears another oscillatory component, which arises from a pole on the pion propagator. This pole is located appart from the axes, giving rise to an oscillating Yukawa-like potential. Therefore, we call this phenomenon 'Yukawa oscillations'. This phenomenon does not appear in the Debye component of the QED screened potential, even if the coupling constant is artificially increased. We have also studied a model of QCD quark-gluon plasma. In this case, the one-gluon propagator also shows this kind of poles. At high densities and/or temperatures, where one expects perturbative QCD to be valid, the pole shifts towards large momenta.
14718218
Nucleon–nucleon effective potential in dense matter including rho-meson exchange
Abstract We obtain the RPA summed one-meson exchange potential between nucleons in symmetric nuclear matter at zero temperature, from a model which includes ρ , σ , ω and π mesons. The behavior of rho mesons inside the medium is first discussed using different schemes to extract a finite contribution from the vacuum polarization. These schemes give qualitatively different results for the in-medium rho mass. The results are discussed in connection with the nonrenormalizability of the model. We next study the modified potential as density increases. In the intermediate-distance range, it is qualitatively modified by matter and vacuum effects. In the long-distance range ( r >2 fm), one observes the presence of oscillations, which are not present in free space. Features on this distance range are insensitive to the renormalization scheme.
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.