Papers by Merced Montesinos
Physical Review D
We study minimal and nonminimal couplings of fermions to the Palatini action in n dimensions (n ≥... more We study minimal and nonminimal couplings of fermions to the Palatini action in n dimensions (n ≥ 3) from the Lagrangian and Hamiltonian viewpoints. The Lagrangian action considered is not, in general, equivalent to the Einstein-Dirac action principle. However, by choosing properly the coupling parameters, it is possible to give a first-order action fully equivalent to the Einstein-Dirac theory in a spacetime of dimension four. By using a suitable parametrization of the vielbein and the connection, the Hamiltonian analysis of the general Lagrangian is given, which involves manifestly Lorentz-covariant phase-space variables, a real noncanonical symplectic structure, and only firstclass constraints. Additional Hamiltonian formulations are obtained via symplectomorphisms, one of them involving half-densitized fermions. To confront our results with previous approaches, the time gauge is imposed.
We study the possibility of applying statistical mechanics to generally covariant quantum theorie... more We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of energy and external time. We consider a composite system formed by a large number of identical components, and apply Boltzmann's ideas and the fundamental postulates of ordinary statistical physics. The thermodynamical parameters are determined by the properties of the thermalizing interaction. We apply these ideas to a simple example, in which the component system has one physical degree of freedom and mimics the constraint algebra of general relativity.
The covariant canonical formalism for four-dimensional BF theory is performed. The aim of the pap... more The covariant canonical formalism for four-dimensional BF theory is performed. The aim of the paper is to understand in the context of the covariant canonical formalism both the reducibility that some first class constraints have in Dirac's canonical analysis and also the role that topological terms play. The analysis includes also the cases when both a cosmological constant and the second Chern character are added to the pure BF action. In the case of the BF theory supplemented with the second Chern character, the presymplectic 3-form is different to the one of the BF theory in spite of the fact both theories have the same equations of motion while on the space of solutions they both agree to each other. Moreover, the analysis of the degenerate directions shows some differences between diffeomorphisms and internal gauge symmetries.
We present a model where early inflation and late accelerating expansion of the Universe are driv... more We present a model where early inflation and late accelerating expansion of the Universe are driven by the real and imaginary parts of a single complex scalar field, which we identified as inflaton and phantom field, respectively. This inflaton-phantom unification is protected by an internal SO(1,1) symmetry, with the two cosmological scalars appearing as the degrees of freedom of a sole fundamental representation. The unification symmetry allows to build successful potentials. We observe that our theory provides a matter-phantom duality, which transforms scalar matter cosmological solutions into phantom solutions and vice versa. We also suggest that a complete unification of all scalar fields of cosmological interest is yet possible under a similar footing.
We present a new BF-type action for complex general relativity with or without a cosmological con... more We present a new BF-type action for complex general relativity with or without a cosmological constant resembling Plebanski's action, which depends on an SO(3,C) connection, a set of 2-forms, a symmetric matrix, and a 4-form. However, it differs from the Plebanski formulation in the way that the symmetric matrix enters into the action. The advantage of this fact is twofold. First, as compared to Plebanski's action, the symmetric matrix can now be integrated out, which leads to a pure BF-type action principle for general relativity; the canonical analysis of the new action then shows that it has the same phase space of the Ashtekar formalism up to a canonical transformation induced by a topological term. Second, a particular choice of the parameters involved in the formulation produces a BF-type action principle describing conformally anti-self-dual gravity. Therefore, the new action unifies both general relativity and anti-self-dual gravity.
After reviewing the covariant description of Hamiltonian dynamics, some applications are done to ... more After reviewing the covariant description of Hamiltonian dynamics, some applications are done to the non-relativistic isotropic three-dimensional harmonic oscillator, Rovelli's model, and SO(3,1) BF theories.
Classical and Quantum Gravity, 2017
In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does n... more In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we claim through an example that flatness is not a sufficient condition to establish the absence of interactions in the underlying microscopic model of a thermodynamic system, which poses a limitation on the usefulness of Ruppeiner's metric and conjecture. Finally, we address the problem of the choice of coordinates in black hole thermodynamics. We propose an alternative energy representation for Kerr-Newman black holes that mimics fully Weinhold's approach. The corresponding Ruppeiner's metrics become degenerate only at absolute zero and have non-vanishing scalar curvatures.
Abstract. An essential step towards the identification of a fermion mass generation mechanism at ... more Abstract. An essential step towards the identification of a fermion mass generation mechanism at the Planck scale is to analyse massive fermions in a given quantum gravity framework. In this letter the two mass terms entering the Hamiltonian constraint for the Einstein-Majorana system are studied in the loop representation of quantum gravity and fermions. One term resembles a bare mass gap because it is not zero for states with zero (fermion) kinetic energy, unlike the other term which is interpreted as 'dressing' the mass. The former contribution originates from (at least) triple intersections of the loop states acted on whilst the latter is traced back to every pair of coinciding end points, where fermions are located. Thus, fermion mass terms get encoded in the combinatorics of loop states. Finally, the possibility is discussed of relating fermion masses to the topology of space. PACS numbers: 0460D, 0420C, 0462 Physics at the Planck length P := Gh/c 3 = 1.6 × 10 −33 cm...
In this paper it is implemented how to make compatible the boundary conditions and the gauge fixi... more In this paper it is implemented how to make compatible the boundary conditions and the gauge fixing conditions for complex general relativity written in terms of Ashtekar variables using the approach of Ref. [1]. Moreover, it is found that at first order in the gauge parameters, the Hamiltonian action is (on shell) fully gauge-invariant under the gauge symmetry generated by the first class constraints in the case when spacetime M has the topology M = R×Σ and Σ has no boundary. Thus, the statement that the constraints linear in the momenta do not contribute to the boundary terms is right, but only in the case when Σ has no boundary. Key words: Ashtekar variables. Boundary conditions. Gauge fixing conditions. It is a common belief that the (internal) gauge symmetry present in Yang-Mills theory is of a different kind with respect to the gauge symmetry involved in generally covariant theories as general relativity. This conclusion comes from the fact that when Yang-Mills theory is expre...
arXiv: General Relativity and Quantum Cosmology, 2020
In this paper we perform in a manifestly $SO(n-1,1)$ [or, alternatively $SO(n)$] covariant fashio... more In this paper we perform in a manifestly $SO(n-1,1)$ [or, alternatively $SO(n)$] covariant fashion, the canonical analysis of general relativity in $n$ dimensions written as a constrained $BF$ theory. Since the Lagrangian action of the theory can be written in two classically equivalent ways, we analyze each case separately. We show that for either action the canonical analysis can be accomplished without introducing second-class constraints during the whole process. Furthermore, in each case the resulting Hamiltonian formulation is the same as the canonical formulation with only first-class constraints recently obtained in M. Montesinos, R. Escobedo, J. Romero, and M. Celada, Phys. Rev. D 101, 024042 (2020) from the $n$-dimensional Palatini action.
General Relativity and Gravitation
We perform, in a manifestly SO(n − 1, 1) [SO(n)] covariant fashion, the Hamiltonian analysis of g... more We perform, in a manifestly SO(n − 1, 1) [SO(n)] covariant fashion, the Hamiltonian analysis of general relativity in n dimensions written as a constrained BF theory. We solve the constraint on the B field in a way naturally adapted to the foliation of the spacetime that avoids explicitly the introduction of the vielbein. This leads to a form of the action involving a presymplectic structure, which is reduced by doing a suitable parametrization of the connection and then, after integrating out some auxiliary fields, the Hamiltonian form involving only first-class constraints is obtained.
Physical Review D
We present a manifestly Lorentz-covariant description of the phase space of general relativity wi... more We present a manifestly Lorentz-covariant description of the phase space of general relativity with the Immirzi parameter. This formulation emerges after solving the second-class constraints arising in the canonical analysis of the Holst action. We show that the new canonical variables give rise to other Lorentz-covariant parametrizations of the phase space via canonical transformations. The resulting form of the first-class constraints in terms of new variables is given. In the time gauge, these variables and the constraints become those found by Barbero.
Physical Review D, 2016
We present a new BF-type action for complex general relativity with or without a cosmological con... more We present a new BF-type action for complex general relativity with or without a cosmological constant resembling Plebanski's action, which depends on an SO(3,C) connection, a set of 2-forms, a symmetric matrix, and a 4-form. However, it differs from the Plebanski formulation in the way that the symmetric matrix enters into the action. The advantage of this fact is twofold. First, as compared to Plebanski's action, the symmetric matrix can now be integrated out, which leads to a pure BFtype action principle for general relativity; the canonical analysis of the new action then shows that it has the same phase space of the Ashtekar formalism up to a canonical transformation induced by a topological term. Second, a particular choice of the parameters involved in the formulation produces a BF-type action principle describing conformally anti-self-dual gravity. Therefore, the new action unifies both general relativity and anti-self-dual gravity.
Physical Review D
We report three manifestly Lorentz-invariant Hamiltonian formulations of minimally and nonminimal... more We report three manifestly Lorentz-invariant Hamiltonian formulations of minimally and nonminimally coupled fermion fields to the Holst action. These formulations are achieved by making a suitable parametrization of both the tetrad and the Lorentz connection, which allows us to integrate out some auxiliary fields without spoiling the local Lorentz symmetry. They have the peculiarity that their noncanonical symplectic structures as well as the phase-space variables for the gravitational sector are real. Moreover, two of these Hamiltonian formulations involve half-densitized fermion fields. We also impose the time gauge on these formulations, which leads to real connections for the gravitational configuration variables. Finally, we perform a symplectomorphism in one of the manifestly Lorentz-invariant Hamiltonian formulations and analyze the resulting formulation, which becomes the Hamiltonian formulation of fermion fields minimally coupled to the Palatini action for particular values of the coupling parameters.
We report a new internal gauge symmetry of the n-dimensional Palatini action with cosmological te... more We report a new internal gauge symmetry of the n-dimensional Palatini action with cosmological term (n > 3) that is the generalization of three-dimensional local translations. This symmetry is obtained through the direct application of the converse of Noether's second theorem on the theory under consideration. We show that diffeomorphisms can be expressed as linear combinations of it and local Lorentz transformations with field-dependent parameters up to terms involving the variational derivatives of the action. As a result, the new internal symmetry together with local Lorentz transformations can be adopted as the fundamental gauge symmetries of general relativity. Although their gauge algebra is open in general, it allows us to recover, without resorting to the equations of motion, the very well-known Lie algebra satisfied by translations and Lorentz transformations in three dimensions. Finally, we report the analog of the new gauge symmetry for the Holst action, finding th...
Classical and Quantum Gravity
1 Departamento de Fısica, Centro de Investigacíon y de Estudios Avanzados del IPN, Av IPN no 2508... more 1 Departamento de Fısica, Centro de Investigacíon y de Estudios Avanzados del IPN, Av IPN no 2508, 07000 Ciudad de Mexico, Mexico 2 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA 3 Centre de Physique Theorique, CNRS, ...
Physical Review D
We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonia... more We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonian constraints. This feature mimics the constraint structure of general relativity, where there is one Hamiltonian constraint associated with each space point. We solve the ...
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Papers by Merced Montesinos