Topology of the Misner space and its g-boundary

The Misner space is a simplified 2-dimensional model of the 4-dimensional Taub-NUT space that reproduces some of its pathological behaviours. In this paper we provide an explicit base of the topology of the complete Misner space ℝ¹,¹/boost. Besides we prove that some parts of this space, that behave like topological boundaries, are equivalent to the g-boundaries of the Misner space.The authors are very grateful to Juan Margalef Roig and Miguel Sánchez Caja for their useful comments and support, and specially to Fernando Barbero and Robert Geroch for their patience, comments and priceless help. This work has been supported by the Spanish MINECO research Grant FIS2012-34379 and the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042)

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)

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)

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

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)

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

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)

On-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries

We study a generalization of the Holst action where we admit nonmetricity and torsion in manifolds with timelike boundaries (both in the metric and tetrad formalism). We prove that its space of solutions is equal to the one of the Palatini action. Therefore, we conclude that the metric sector is in fact identical to general relativity (GR), which is defined by the Einstein-Hilbert action. We further prove that, despite defining the same space of solutions, the Palatini and (the generalized) Holst Lagrangians are not cohomologically equal. Thus, the presymplectic structure and charges provided by the covariant phase space method might differ. However, using the relative bicomplex framework, we show the covariant phase spaces of both theories are equivalent (and in fact equivalent to GR), as well as their charges, clarifying some open problems regarding dual charges and their equivalence in different formulations.This work has been supported by the Spanish Ministerio de Ciencia Innovación y Universidades-Agencia Estatal de Investigación FIS2017-84440-C2-2-P and PID2020-116567GB-C22 grants. Juan Margalef-Bentabol is supported by the AARMS postdoctoral fellowship, by the NSERC Discovery Grant No. 2018-04873, and the NSERC Grant RGPIN-2018-04887. E.J.S. Villaseñor is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation)

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

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