arXiv subjects

Alejandro Perez

Publications and source records attributed to Alejandro Perez.

At least 73 records · Page 4Linked to original sources

arXiv2011

The SU(2) Black Hole entropy revisited

We study the state-counting problem that arises in the SU(2) black hole entropy calculation in loop quantum gravity. More precisely, we compute the leading term and the logarithmic correction of both the spherically symmetric and the distorted SU(2) black holes. Contrary to what has been done in previous works, we have to take into account "quantum corrections" in our framework in the sense that the level k of the Chern-Simons theory which describes the black hole is finite and not sent to infinity. Therefore, the new results presented here allow for the computation of the entropy in models where the quantum group corrections are important.

gr-qc↗

arXiv2010

Rare B decays Potential of SuperB

The study of rare B-decays at SuperB provides unique opportunities to understand the Standard Model and constrain new physics. It is discussed the new physics potential of the B -> K nu nu_bar and B -> K^{\ast} nu nu_bar system from the proposed SuperB experiment with 75ab-1 of data (5 nominal years of data taking).

hep-ex↗

arXiv2010

Black hole entropy and SU(2) Chern-Simons theory

Black holes in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with marked points. Moreover, the counting can be mapped to counting the number of SU(2) intertwiners compatible with the spins that label the defects. The resulting BH entropy is proportional to a_H with logarithmic corrections ΔS=-3/2 \log a_H. Our treatment from first principles completely settles previous controversies concerning the counting of states.

gr-qc↗

arXiv2010

Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons

A detailed analysis of the spherically symmetric isolated horizon system is performed in terms of the connection formulation of general relativity. The system is shown to admit a manifestly SU(2) invariant formulation where the (effective) horizon degrees of freedom are described by an SU(2) Chern-Simons theory. This leads to a more transparent description of the quantum theory in the context of loop quantum gravity and modifications of the form of the horizon entropy.

gr-qc↗

arXiv2010

A topological limit of gravity admitting an SU(2) connection formulation

We study the Hamiltonian formulation of the generally covariant theory defined by the Lagrangian 4-form L=e_I e_J F^{IJ}(ω) where e^I is a tetrad field and F^{IJ} is the curvature of a Lorentz connection ω^{IJ}. This theory can be thought of as the limit of the Holst action for gravity for the Newton constant G goes to infinity and Immirzi parameter goes to zero, while keeping their product fixed. This theory has for a long time been conjectured to be topological. We prove this statement both in the covariant phase space formulation as well as in the standard Dirac formulation. In the time gauge, the unconstrained phase space of theory admits an SU(2) connection formulation which makes it isomorphic to the unconstrained phase space of gravity in terms of Ashtekar-Barbero variables. Among possible physical applications, we argue that the quantization of this topological theory might shed new light on the nature of the degrees of freedom that are responsible for black entropy in loop quantum gravity.

gr-qc↗

arXiv2010

On the regularization of the constraints algebra of Quantum Gravity in 2+1 dimensions with non-vanishing cosmological constant

We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful in the Lambda=0 case and widely applied in four dimensional LQG) lead 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 non-local nature of generalized connections.

gr-qc↗

arXiv2009

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 spacetime 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 depend 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.

gr-qc↗

arXiv2009

Spin Foam Quantization and Anomalies

The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are left open to choice. Since their large-spin behavior determines the convergence properties of the state-sum, this gap has to be closed before any reliable conclusion about finiteness can be reached. It is shown that these amplitudes are directly related to the path integral measure and can in principle be derived from it, requiring detailed knowledge of the constraint algebra and gauge fixing. In a related manner, minimal requirements of background independence provide non trivial restrictions on the form of an anomaly free measure. Many models in the literature do not satisfy these requirements. A simple model satisfying the above consistency requirements is presented which can be thought of as a spin foam quantization of the Husain--Kuchar model.

gr-qc↗

arXiv2009

4d Lorentzian Holst action with topological terms

We study the Hamiltonian formulation of the general first order action of general relativity compatible with local Lorentz invariance and background independence. The most general simplectic structure (compatible with diffeomorphism invariance and local Lorentz transformations) is obtained by adding to the Holst action the Pontriagin, Euler and Nieh-Yan invariants with independent coupling constants. We perform a detailed canonical analysis of this general formulation (in the time gauge) exploring the structure of the phase space in terms of connection variables. We explain the relationship of these topological terms, and the effect of large SU(2) gauge transformations in quantum theories of gravity defined in terms of the Ashtekar-Barbero connection.

gr-qc↗

arXiv2008

On the symmetry of the vacuum in theories with spontaneous symmetry breaking

We review the usual account of the phenomena of spontaneous symmetry breaking (SSB), pointing out the common misunderstandings surrounding the issue, in particular within the context of quantum field theory. In fact, the common explanations one finds in this context, indicate that under certain conditions corresponding to the situation called SSB, the vacuum of the theory does not share the symmetries of the Lagrangian. We explain in detail why this statement is incorrect in general, and in what limited set of circumstances such situation could arise. We concentrate on the case of global symmetries, for which we found no satisfactory exposition in the existing literature, and briefly comment on the case of gauge symmetries where, although insufficiently publicized, accurate and complete descriptions exist. We briefly discuss the implications for the phenomenological manifestations usually attributed to the phenomena of spontaneous symmetry breaking, analyzing which might be affected by our analysis and which are not. In particular we describe the mass generation mechanism in a fully symmetric scheme (i.e., with a totally symmetric vacuum), and briefly discuss the implications of this analysis to the problem of formation of topological defects in the early universe.

physics.gen-ph↗

arXiv2007

Cosmological Plebanski theory

We consider the cosmological symmetry reduction of the Plebanski action as a toy-model to explore, in this simple framework, some issues related to loop quantum gravity and spin-foam models. We make the classical analysis of the model and perform both path integral and canonical quantizations. As for the full theory, the reduced model admits two types of classical solutions: topological and gravitational ones. The quantization mixes these two solutions, which prevents the model to be equivalent to standard quantum cosmology. Furthermore, the topological solution dominates at the classical limit. We also study the effect of an Immirzi parameter in the model.

gr-qc↗

arXiv2007

The theta parameter in loop quantum gravity: effects on quantum geometry and black hole entropy

The precise analog of the theta-quantization ambiguity of Yang-Mills theory exists for the real SU(2) connection formulation of general relativity. As in the former case theta labels representations of large gauge transformations, which are super-selection sectors in loop quantum gravity. We show that unless theta=0, the (kinematical) geometric operators such as area and volume are not well defined on spin network states. More precisely the intersection of their domain with the dense set Cyl in the kinematical Hilbert space H of loop quantum gravity is empty. The absence of a well defined notion of area operator acting on spin network states seems at first in conflict with the expected finite black hole entropy. However, we show that the black hole (isolated) horizon area--which in contrast to kinematical area is a (Dirac) physical observable--is indeed well defined, and quantized so that the black hole entropy is proportional to the area. The effect of theta is negligible in the semiclassical limit where proportionality to area holds.

gr-qc↗

arXiv2007

Two-dimensional topological field theories coupled to four-dimensional BF theory

Four dimensional BF theory admits a natural coupling to extended sources supported on two dimensional surfaces or string world-sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two dimensional world-sheet. We show how two dimensional Yang-Mills degrees of freedom can be added on the world-sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world-sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background independent quantum field theory where local degrees of freedom at low energies arise from global topological (world-sheet) degrees of freedom at the fundamental level.

gr-qc↗

arXiv2007

Extended matter coupled to BF theory

Recently, a topological field theory of membrane-matter coupled to BF theory in arbitrary spacetime dimensions was proposed [1]. In this paper, we discuss various aspects of the four-dimensional theory. Firstly, 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). Secondly, 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.

gr-qc↗

arXiv2007

Multiple-event probability in general-relativistic quantum mechanics: 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. We consider a version of the model with unitary time-evolution and a version without unitary time-evolution

gr-qc↗

arXiv2007

Mean field exact solutions showing charge density wave crossover at low fillings in the fractional quantum Hall regime

A general analytical framework for the determination of the mean field states at arbitrary rational filling factors for the 2DEG in FQHE regime is given. Its use allows to obtain analytic expressions for the solutions at filling factors of the form $ν=1/q$ for arbitrary odd $q$. The analysis can be performed for two general classes of states characterized by $γ=1$ or $γ={1/2}$ particles per unit cell. Instead of the periodic peaks of the Wigner solid solution, the new states show electron densities forming percolating ridges that may favor an energy decrease through correlated ring of exchange contributions. Therefore, we estimate that they can realize mean field versions of the so called Hall Crystal (HC) states. The obtained analytic HC solution shows the same crystalline symmetry that the corresponding WC state in its class $γ=1$, but a qualitatively different charge density distribution. The energy dependence of the corresponding HC and WC states on the filling factor is also evaluated here for the class $γ=1/2$. The results show a crossover between HC state and the Wigner crystal, close to filling 1/7. Therefore, transitions may occur from one to the other as the electron density is varied. This result is consistent with recent experimental findings.

cond-mat.mes-hall↗

arXiv2006

Multiple-event probability in general-relativistic quantum mechanics

We discuss the definition of quantum probability in the context of "timeless" general--relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multi-event probability. In conventional quantum mechanics this can be obtained by means of the ``wave function collapse" algorithm. We first point out certain difficulties of some natural definitions of multi-event probability, including the conditional probability widely considered in the literature. We then observe that multi-event probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum classical boundary, one can always trade a sequence of non-commuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the "wave function collapse" algorithm can nevertheless be recovered. The discussion bears also on the nature of the quantum collapse.

gr-qc↗

arXiv2006

Quantization of strings and branes coupled to BF theory

BF theory is a topological theory that can be seen as a natural generalization of 3-dimensional gravity to arbitrary dimensions. Here we show that the coupling to point particles that is natural in three dimensions generalizes in a direct way to BF theory in d dimensions coupled to (d-3)-branes. In the resulting model, the connection is flat except along the membrane world-sheet, where it has a conical singularity whose strength is proportional to the membrane tension. As a step towards canonically quantizing these models, we show that a basis of kinematical states is given by `membrane spin networks', which are spin networks equipped with extra data where their edges end on a brane.

gr-qc↗