The thermodynamic limit for black holes in loop quantum gravity

This contribution discusses the thermodynamic limit for black holes in loopquantum gravity by using the number-theoretic methods introduced to compute their entropy in this framework. We show how that the subdominant corrections for the entropy in this limit differ from the ones corresponding to the statistical entropy.This work has been supported by the Spanish MICINN research grants FIS2009-11893, FIS2012-34379 and the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042)

Separable Hilbert space for loop quantization

We discuss, within the simplified context provided by the polymeric harmonic oscillator, a construction leading to a separable Hilbert space that preserves some of the most important features of the spectrum of the Hamiltonian operator. This construction may be applied to other polymer quantum mechanical systems, including those of loop quantum cosmology, and is likely generalizable to certain formulations of full loop quantum gravity. It is helpful to sidestep some of the physically relevant issues that appear in that context, in particular those related to superselection and the definition of suitable ensembles for the statistical mechanics of these types of systems.This work has been supported by the Spanish MICINN and MINECO research Grants No. FIS2009-11893, No. FIS2011-30145-C03-02, No. FIS2012-34379 and the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042), Chilean FONDECYT regular Grant No. 1140335 as well as by the National Center for Science (NCN) of Poland research Grants No. 2012/05/E/ST2/03308 and No. 2011/02/A/ST2/00300. T. P. also acknowledges the financial support of UNAB via internal project No. DI-562-14/R

Quantum Einstein-Rosen waves: coherent states and n-point functions

We discuss two different types of issues concerning the quantization of Einstein Rosen waves. First we study in detail the possibility of using the coherent states corresponding to the dynamics of the auxiliary, free Hamiltonian appearing in the description of the model to study the full dynamics of the system. For time periods of arbitrary length we show that this is only possible for states that are close, in a precise mathematical sense, to the vacuum. We do this by comparing the quantum evolutions defined by the auxiliary and physical Hamiltonians on the class of coherent states. In the second part of the paper we study the structure of n-point functions. As we will show their detailed behavior differs from that corresponding to standard perturbative quantum field theories. We take this as a manifestation of the fact that the correct approximation scheme for physically interesting objects in these models does not lead to a power series expansion in the relevant coupling constant but to a more complicated asymptotic behavior.The authors want to thank Daniel Gómez Vergel for his comments and careful reading of the manuscript. IG acknowledges the financial support provided by the Spanish Ministry of Science and Education (MEC) under the FPU program. This work is also supported by the Spanish MEC under the research grant FIS2005-05736-C03-02

Gauge invariance in simple mechanical systems

This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or graduate students in theoretical physics to understand, in a familiar context, some concepts relevant to the study of classical and quantum field theories. We use a geometric approach to derive the Hamiltonian formulation for the model considered in the paper: four equal masses connected by six ideal rods. We obtain and discuss the meaning of several important elements, in particular, the constraints and the Hamiltonian vector fields that define the dynamics of the system, the constraint manifold, gauge symmetries, gauge orbits, gauge fixing, and the reduced phase space.The authors want to thank Juan Margalef and Mariano Santander for their useful comments. This work has been supported by the Spanish MINECO research grants FIS2012-34379, FIS2014-57387-C3-3-P and the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042)

Band structure in the polymer quantization of the harmonic oscillator

We discuss the detailed structure of the spectrum of the Hamiltonian for the polymerized harmonic oscillator and compare it with the spectrum in the standard quantization. As we will see the non-separability of the Hilbert space implies that the point spectrum consists of bands similar to the ones appearing in the treatment of periodic potentials. This feature of the spectrum of the polymeric harmonic oscillator may be relevant for the discussion of the polymer quantization of the scalar field and may have interesting consequences for the statistical mechanics of these models.We would like to thank W Chojnacki, A Corichi, J Lewandowski, T Pawłowski, P Singh and M Varadarajan for their valuable comments. This work has been supported by the Spanish MICINN research grants FIS2009-11893, FIS2012-34379 and the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042)

Hamiltonian treatment of linear field theories in the presence of boundaries: A geometric approach

The purpose of this paper is to study in detail the constraint structure of the Hamiltonian description for the scalar and electromagnetic fields in the presence of spatial boundaries. We carefully discuss the implementation of the geometric constraint algorithm of Gotay, Nester and Hinds with special emphasis on the relevant functional analytic aspects of the problem. This is an important step toward the rigorous understanding of general field theories in the presence of boundaries, very especially when these fail to be regular. The geometric approach employed in the paper is also useful with regard to the interpretation of the physical degrees of freedom and the nature of the constraints when both gauge symmetries and boundaries are present.The authors want to thank M Gotay and, especially, J Nester for their useful comments. This work has been supported by the Spanish MICINN research grants FIS2009-11893, FIS2012-34379 and the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042)

Hamiltonian dynamics of the parametrized electromagnetic field

We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.This work has been supported by the Spanish MINECO research grants FIS2012-34379, FIS2014-57387-C3-3-P and the Consolider-Ingenio 2010 Program CPAN (CSD 2007-00042). Juan Margalef-Bentabol is supported by a ‘la Caixa’ fellowship

Hamiltonian description of the parametrized scalar field in bounded spatial regions

We study the Hamiltonian formulation for a parametrized scalar field in a regular bounded spatial region subject to Dirichlet, Neumann and Robin boundary conditions. We generalize the work carried out by a number of authors on parametrized field systems to the interesting case where spatial boundaries are present. The configuration space of our models contains both smooth scalar fields defined on the spatial manifold and spacelike embeddings from the spatial manifold to a target spacetime endowed with a fixed Lorentzian background metric. We pay particular attention to the geometry of the infinite dimensional manifold of embeddings and the description of the relevant geometric objects: the symplectic form on the primary constraint submanifold and the Hamiltonian vector fields defined on it.This work has been supported by the Spanish MINECO research grants FIS2012-34379, FIS2014-57387-C3-3-P and the Consolider-Ingenio 2010 Program CPAN (CSD 2007-00042). Juan Margalef-Bentabol is supported by a 'la Caixa' fellowship

Functional evolution of scalar fields in bounded one-dimensional regions

We discuss the unitarity of the quantum evolution between arbitrary Cauchy surfaces of a 1 + 1 dimensional free scalar field defined on a bounded spatial region and subject to several types of boundary conditions including Dirichlet, Neumann and Robin.The authors wish to thank Ivan Agullo and Madhavan Varadarajan for their valuable comments. This work has been supported by the Spanish MINECO research grant FIS2014-57387-C3-3-P. Juan Margalef-Bentabol is supported by a 'la Caixa' fellowship and a Residencia de Estudiantes (MINECO) fellowship

Adiabatic expansions for Dirac fields, renormalization, and anomalies

We introduce an iterative method to univocally determine the adiabatic expansion of the modes of Dirac fields in spatially homogeneous external backgrounds. We overcome the ambiguities found in previous studies and use this new procedure to improve the adiabatic regularization/renormalization scheme. We provide details on the application of the method for Dirac fields living in a four-dimensional Friedmann-Lemaître-Robertson-Walker spacetime with a Yukawa coupling to an external scalar field. We check the consistency of our proposal by working out the conformal anomaly. We also analyze a two-dimensional Dirac field in Minkowski space coupled to a homogeneous electric field and reproduce the known results on the axial anomaly. The adiabatic expansion of the modes given here can be used to properly characterize the allowed physical states of the Dirac fields in the above external backgrounds.This work has been supported by the Spanish MINECO research grants FIS2014-57387-C3-3-P; FIS2014-57387-C3-1-P; FIS2017-84440-C2-2-P; FIS2017-84440-C2-1-P, the COST action CA15117 (CANTATA), supported by COST (European Cooperation in Science and Technology), and the Severo Ochoa Program SEV-2014-0398. A. F. is supported by the Severo Ochoa Ph.D. fellowship SEV-2014-0398-16-1 and the European Social Fund