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.
118591329
Extended matter coupled to BF theory
Recently, a topological field theory of membrane matter coupled to BF theory in arbitrary spacetime dimensions was proposed [J. C. Baez and A. Perez, Adv. Theor. Math. Phys. 11, 3 (2007).]. In this paper, we discuss various aspects of the four-dimensional theory. First, we study classical solutions leading to an interpretation of the theory in terms of strings propagating on a flat spacetime. We also show that the general classical solutions of the theory are in one-to-one correspondence with solutions of Einstein's equations in the presence of distributional matter (cosmic strings). Second, we quantize the theory and present, in particular, a prescription to regularize the physical inner product of the canonical theory. We show how the resulting transition amplitudes are dual to evaluations of Feynman diagrams coupled to three-dimensional quantum gravity. Finally, we remove the regulator by proving the topological invariance of the transition amplitudes.
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.
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.
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.
13891330
Spin foam models for quantum gravity
In this topical review, we review the present status of the spin foam formulation of non-perturbative (background-independent) quantum gravity. The topical review is divided into two parts. In the first part, we present a general introduction to the main ideas emphasizing their motivation from various perspectives. Riemannian three-dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for four-dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four dimensions (gauge invariance, discretization independence, etc). In the second part, we concentrate on the definition of the Barrett–Crane model. We present the main results obtained in this framework from a critical perspective. Finally, we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the Barrett–Crane model in this framework and review the finiteness results obtained for both its Riemannian and its Lorentzian variants.
118389125
Even-dimensional topological gravity from Chern–Simons gravity
Abstract It is shown that the topological action for gravity in 2 n -dimensions can be obtained from the ( 2 n + 1 ) -dimensional Chern–Simons gravity genuinely invariant under the Poincare group. The 2 n -dimensional topological gravity is described by the dynamics of the boundary of a ( 2 n + 1 ) -dimensional Chern–Simons gravity theory with suitable boundary conditions. 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 ) .
119684059
Analytic behavior of the QED polarizability function at finite temperature
We revisit the analytical properties of the static quasi-photon polarizability function for an electron gas at finite temperature, in connection with the existence of Friedel oscillations in the potential created by an impurity. In contrast with the zero temperature case, where the polarizability is an analytical function, except for the two branch cuts which are responsible for Friedel oscillations, at finite temperature the corresponding function is non analytical, in spite of becoming continuous everywhere on the complex plane. This effect produces, as a result, the survival of the oscillatory behavior of the potential. We calculate the potential at large distances, and relate the calculation to the non-analytical properties of the polarizability.
119094287
Equilibrium properties of self-interacting neutrinos in the quasi-particle approach
In this work, a neutrino gas in equilibrium is studied both at T = 0 and at finite temperature. Neutrinos are treated as massive Dirac quasi-particles with two generations. We include self-interactions among the neutrinos via neutral currents, as well as the interaction with a background of matter. To obtain the equilibrium properties, we use Wigner function techniques. To account for corrections beyond the Hartree approximation, we also introduce correlation functions. We prove that, under the quasi-particle approximation, these correlation functions can be expressed as products of Wigner functions. We analyse the main properties of the neutrino eigenmodes in the medium, such as effective masses and mixing angle. We show that the formulae describing these quantities will differ with respect to the case with no self-interactions.
35052453
Relativistic approach to positronium levels in a strong magnetic field
We have investigated the bound states of an electron and positron in superstrong magnetic fields typical for neutron stars. The complete relativistic problem of positronium in a strong magnetic field has not been succesfully solved up to now. In particular, we have studied the positronium when it moves relativistically across the magnetic field. A number of problems which deal with the pulsar magnetosphere, as well as the evolution of protoneutron stars, could be considered as a field for application.
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 ) .