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Merced Montesinos

Publications and source records attributed to Merced Montesinos.

At least 55 records · Page 3Linked to original sources
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

BF gravity with Immirzi parameter and cosmological constant

The action principle of the BF type introduced by Capovilla, Montesinos, Prieto, and Rojas (CMPR) which describes general relativity with Immirzi parameter is modified in order to allow the inclusion of the cosmological constant. The resulting action principle is on the same footing as the original Plebanski action in the sense that the equations of motion coming from the new action principle are equivalent to the Holst action principle plus a cosmological constant without the need of imposing additional restrictions on the fields. We consider this result a relevant step towards the coupling of matter fields to gravity in the framework of the CMPR action principle.

gr-qc↗
arXiv2009

Husain-Kuchar model as a constrained BF theory

The Husain-Kuchar theory is a four-dimensional background-independent model that has long been viewed as a useful model for addressing several conceptual and technical problems appearing in the quantization of general relativity mainly in the loop quantum gravity approach. The model was defined at Lagrangian level in terms of a su(2)-valued connection one-form $A$ coupled through its curvature to a su(2)-valued one-form field $e$. We address here the problem of writing a Lagrangian formulation for the Husain-Kuchar model as a constrained BF theory motivated by the fact that spin foam models for quantum gravity are related to action principles of the BF type. The Lagrangian action principle for the Husain-Kuchar model reported here differs from a previous one found by Barbero et al in that this description involves a single constrained BF theory rather than two interacting BF theories. It is, essentially, the Plebanski action with the condition on the trace of the Lagrange multipliers removed. Moreover, it can be stated that the relationship between our BF-like action and the original one for the Husain-Kuchar model is the same relationship that exists between the Plebanski action and the self-dual Palatini action for complex general relativity, first because the solution to the constraint on the two-forms $Σ^i$ coming from the BF-like action leads to the Husain-Kuchar action, and second because the Hamiltonian analysis of the Husain-Kuchar model is straightforward starting from the BF-like action principle.

gr-qc↗
arXiv2008

Topological field theories in n-dimensional spacetimes and Cartan's equations

Action principles of the BF type for diffeomorphism invariant topological field theories living in n-dimensional spacetime manifolds are presented. Their construction is inspired by Cuesta and Montesinos' recent paper where Cartan's first and second structure equations together with first and second Bianchi identities are treated as the equations of motion for a field theory. In opposition to that paper, the current approach involves also auxiliary fields and holds for arbitrary n-dimensional spacetimes. Dirac's canonical analysis for the actions is detailedly carried out in the generic case and it is shown that these action principles define topological field theories, as mentioned. The current formalism is a generic framework to construct geometric theories with local degrees of freedom by introducing additional constraints on the various fields involved that destroy the topological character of the original theory. The latter idea is implemented in two-dimensional spacetimes where gravity coupled to matter fields is constructed out, which has indeed local excitations.

gr-qc↗
arXiv2008

Unification of cosmological scalar fields

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.

astro-ph↗
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↗
arXiv2006

Gauge systems with noncommutative phase space

Some very simple models of gauge systems with noncanonical symplectic structures having $sl(2,r)$ as the gauge algebra are given. The models can be interpreted as noncommutative versions of the usual $SL(2,\mathbb{R})$ model of Montesinos-Rovelli-Thiemann. The symplectic structures of the noncommutative models, the first-class constraints, and the equations of motion are those of the usual $SL(2,\mathbb{R})$ plus additional terms that involve the parameters $θ^{μν}$ which encode the noncommutativity among the coordinates plus terms that involve the parameters $Θ_{μν}$ associated with the noncommutativity among the momenta. Particularly interesting is the fact that the new first-class constraints get corrections linear and quadratic in the parameters $θ^{μν}$ and $Θ_{μν}$. The current constructions show that noncommutativity of coordinates and momenta can coexist with a gauge theory by explicitly building models that encode these properties. This is the first time models of this kind are reported which might be significant and interesting to the noncommutative community.

hep-th↗
arXiv2006

Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories

The most general action, quadratic in the B fields as well as in the curvature F, having SO(3,1) or SO(4) as the internal gauge group for a four-dimensional BF theory is presented and its symplectic geometry is displayed. It is shown that the space of solutions to the equations of motion for the BF theory can be endowed with symplectic structures alternative to the usual one. The analysis also includes topological terms and cosmological constant. The implications of this fact for gravity are briefly discussed.

gr-qc↗
arXiv2006

Covariant canonical formalism for four-dimensional BF theory

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.

gr-qc↗
arXiv2006

Symmetric energy-momentum tensor in Maxwell, Yang-Mills, and Proca theories obtained using only Noether's theorem

The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to this end.

hep-th↗
arXiv2006

Linear constraints from generally covariant systems with quadratic constraints

How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with previous works which use infinitesimal ones. Two kinds of variational principles are taken into account; the first one features non-gauge-invariant actions whereas the second includes fully gauge-invariant actions. Furthermore, it is shown that it is possible to rewrite fully gauge-invariant actions featuring first class constraints quadratic in the momenta into first class constraints linear in the momenta (and homogeneous in some cases) due to the full gauge invariance of their actions. This shows that the gauge symmetry present in generally covariant theories having first class constraints quadratic in the momenta is not of a different kind with respect to the one of theories with first class constraints linear in the momenta if fully gauge-invariant actions are taken into account for the former theories. These ideas are implemented for the parametrized relativistic free particle, parametrized harmonic oscillator, and the SL(2,R) model.

gr-qc↗
arXiv2006

Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures

A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of second-class constraints in the formalism which are handled using the procedure of Rothe and Scholtz recently reported. The current method is applied to the nonrelativistic two-dimensional isotropic harmonic oscillator employing the various symplectic structures for this dynamical system recently reported.

gr-qc↗
arXiv2006

Covariant description of parametrized nonrelativistic Hamiltonian systems

The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism there exists a freedom in the choice of the symplectic structure on the extended phase space and in the choice of the equations that define the constraint surface with the only restriction that these two choices combine in such a way that any pair (of these two choices) generates the same gauge transformation. The consequence of this freedom on the algebra of observables is also discussed.

gr-qc↗
arXiv2004

Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty

We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the application of Dirac's quantization rule to the various symplectic structures recently reported for this classical system. It is pointed out that that these quantum theories are inequivalent in the sense that the mean values for the operators (observables) associated with the same physical classical observable do not agree with each other. The inequivalence does not arise from ambiguities in the ordering of operators but from the fact of having several symplectic structures defined with respect to the same set of coordinates. It is also shown that the uncertainty relations between the fundamental observables depend on the particular quantum theory chosen. It is important to emphasize that these (somehow paradoxical) results emerge from the combination of two paradigms: Dirac's quantization rule and the usual Copenhagen interpretation of quantum mechanics.

quant-ph↗
arXiv2003

The double role of Einstein's equations: as equations of motion and as vanishing energy-momentum tensor

Diffeomorphism covariant theories with dynamical background metric, like gravity coupled to matter fields in the way expressed by Einstein-Hilbert's action or relativistic strings described by Polyakov's action, have `on-shell' vanishing energy-momentum tensor $t_{μν}$ because $t_{μν}$ is, essentially, the Eulerian derivative associated with the dynamical background metric and thus $t_{μν}$ vanishes `on-shell.' Therefore, the equations of motion for the dynamical background metric play a double role: as equations of motion themselves and as a reflection of the fact that $t_{μν}=0$. Alternatively, the vanishing property of $t_{μν}$ can be seen as a reflection of the so-called `problem of time' present in diffeomorphism covariant theories in the sense that $t_{μν}$ are written as linear combinations of first class constraints only.

gr-qc↗
arXiv2001

Bosonic string theory with constraints linear in the momenta

The Hamiltonian analysis of Polyakov action is reviewed putting emphasis in two topics: Dirac observables and gauge conditions. In the case of the closed string it is computed the change of its action induced by the gauge transformation coming from the first class constraints. As expected, the Hamiltonian action is not gauge invariant due to the Hamiltonian constraint quadratic in the momenta. However, it is possible to add a boundary term to the original action to build a fully gauge-invariant action at first order. In addition, two relatives of string theory whose actions are fully gauge-invariant under the gauge symmetry involved when the spatial slice is closed are built. The first one is pure diffeomorphism in the sense it has no Hamiltonian constraint and thus bosonic string theory becomes a sub-sector of its space of solutions. The second one is associated with the tensionless bosonic string, its boundary term induces a canonical transformation and the fully gauge-invariant action written in terms of the new canonical variables becomes linear in the momenta.

hep-th↗
arXiv2001

Self-dual gravity with topological terms

The canonical analysis of the (anti-) self-dual action for gravity supplemented with the (anti-) self-dual Pontrjagin term is carried out. The effect of the topological term is to add a `magnetic' term to the original momentum variable associated with the self-dual action leaving the Ashtekar connection unmodified. In the new variables, the Gauss constraint retains its form, while both vector and Hamiltonian constraints are modified. This shows, the contribution of the Euler and Pontrjagin terms is not the same as that coming from the term associated with the Barbero-Immirzi parameter, and thus the analogy between the theta-angle in Yang-Mills theory and the Barbero-Immirzi parameter of gravity is not appropriate.

gr-qc↗