arXiv subjects

Alberto Escalante

Publications and source records attributed to Alberto Escalante.

At least 19 recordsLinked to original sources

arXiv2025

Canonical description of Pontryagin and Euler classes with a Barbero-Immirzi parameter

A detailed canonical analysis for Pontryagin and Euler classes with a Barbero-Immirzi [BI] parameter is developed. We rewrite the topological invariants by introducing a set of Holst-like variables, and then study the set of all constraints. We report the complete canonical structure and the symmetries of the theory; we count the physical degrees of freedom and identify reducibility conditions among the constraints. In addition, in our results, if we consider the $BI$ parameter takes the value of $\gamma = \pm i $, then the self-dual representation of these invariants is reproduced. Finally, we couple the invariants to the Holst action and explore the canonical analysis.

gr-qc↗

arXiv2025

Characteristic equations of linearized $\lambda R$ gravity

A detailed Hamilton-Jacobi analysis for linearized $\lambda R$ gravity is developed. The model is constructed by rewriting linearized gravity in terms of a parameter $\lambda$ and new variables. The set of all hamiltonians is identified successfully, and the fundamental differential is established. The non-involutive hamiltonians are eliminated, and the Hamilton-Jacobi generalized brackets are calculated. Such brackets are used to report the characteristic equations, and the counting of the number of degrees of freedom is performed. We fixed the gauge to indicate an intimate closeness between the model under study and linearized gravity.

gr-qc↗

arXiv2024

New canonical analysis for consistent extension of $λR$ gravity

The canonical analysis of the $λR$ model extended with the term due to Blas, Pujolas, and Sibiryakov $[BPS]$ is performed. The analysis is developed for any value of $λ$, but particular attention is paid to the point $λ=\frac{1}{3}$ because of the closeness with linearized General Relativity [GR]. Then, we add the higher-order conformal term, the so-called Cotton-square term, to study the constraint structure of what constitutes an example of kinetic-conformal Horava's gravity. At the conformal point, an extra second-class constraint appears; this does not arise at other values of $λ$. Then, the Dirac brackets are constructed, and we will observe that the $λR$-Cotton-square model shares the same number of degrees of freedom with linearized $GR$.

gr-qc↗

arXiv2024

Canonical analysis of linearized $λR$ gravity plus a Chern-Simons term

The Hamiltonian analysis for the linearized $λR$ gravity plus a Chern-Simons term is performed. The first-class and second-class constraints for arbitrary values of $λ$ are presented, and one physical degree of freedom is reported. The second-class constraints are removed, and the corresponding generalized Dirac brackets are constructed; then, the difference between theories with different values of $λ$ is remarked.

gr-qc↗

arXiv2024

Hamiltonian analysis for perturbative $λR$ gravity

The Hamiltonian analysis for the linearized $λR$ gravity around the Minkowski background is performed. The first-class and second-class constraints for arbitrary values of $λ$ are presented, and two physical degrees of freedom are reported. In addition, we remove the second-class constraints, and the generalized Dirac brackets are constructed; then, the equivalence between General Relativity and the $λR$ theory is shown.

gr-qc↗

arXiv2023

Hamiltonian analysis for new massive gravity

A detailed canonical analysis for three-dimensional massive gravity is performed. The construction of the fundamental Dirac brackets, the complete structure of the constraints and the counting of the physical degrees of freedom are reported. In addition, it is shown that the extended Hamiltonian is healed from Orstrogradki's instabilities.

gr-qc↗

arXiv2023

Analysis of linearized Weyl gravity via the Hamilton-Jacobi method

The Hamilton-Jacobi formalism is used to analyze the Weyl theory in the weak-field limit. The complete set of involutive Hamiltonians is obtained, which are classified into involutive and non-involutive. The counting of degrees of freedom is performed. Additionally, the generalized brackets and gauge symmetries are reported.

gr-qc↗

arXiv2023

Canonical analysis for Chern-Simons modification of general relativity

By using the Gitman-Lyakhovich-Tyutin canonical analysis for higher-order theories a four-dimensional Chern-Simons modification of general relativity is analyzed. The counting of physical degrees of freedom, the symmetries, and the fundamental Dirac brackets are reported. Additionally, we report the complete structure of the constraints and its Dirac algebra is developed.

gr-qc↗

arXiv2023

The Hamilton-Jacobi analysis for higher-order modified gravity

The Hamilton-Jacobi $[HJ]$ study for the Chern-Simons $[CS]$ modification of general relativity $[GR]$ is performed. The complete structure of the Hamiltonians and the generalized brackets are reported, from these results the $HJ$ fundamental differential is constructed and the symmetries of the theory are found. By using the Hamiltonians we remove an apparent Ostrogradsky's instability and the new structure of the hamiltonian is reported. In addition, the counting of physical degrees of freedom is developed and some remarks are discussed.

gr-qc↗

arXiv2021

The Hamilton-Jacobi analysis for higher-order Chern-Simons gravity

The Hamilton-Jacobi [$HJ$] analysis for higher-order Chern-Simons gravity is performed. The complete set of $HJ$ Hamiltonians are identified and a fundamental $HJ$ differential is constructed, from which the characteristic equations are obtained. In addition, the symmetries of the theory are identified and the obtained results are compared with other approaches reported in the literature.

math-ph↗

arXiv2021

The Hamilton-Jacobi analysis for higher order Maxwell-Chern-Simons gauge theory

By using the Hamilton-Jacobi [$HJ$] framework the higher-order Maxwell-Chern-Simons theory is analyzed. The complete set of $HJ$ Hamiltonians and a generalized $HJ$ differential are reported, from which all symmetries of the theory are identified. In addition, we complete our study by performing the higher order Gitman-Lyakhovich-Tyutin [$GLT$] framework and compare the results of both formalisms.

hep-th↗

arXiv2020

The Hamilton-Jacobi characteristic equations for three dimensional Ashtekar gravity

The Hamilton-Jacobi analysis of three dimensional gravity defined in terms of Ashtekar-like variables is performed. We report a detailed analysis where the complete set of Hamilton-Jacobi constraints, the characteristic equations and the gauge transformations of the theory are found. We find from integrability conditions on the Hamilton-Jacobi Hamiltonians that the theory is reduced to a $BF$ field theory defined only in terms of self-dual (or anti-self-dual) variables; we identify the dynamical variables and the counting of physical degrees of freedom is performed. In addition, we compare our results with those reported by using the canonical formalism.

gr-qc↗

arXiv2019

The Hamilton-Jacobi characteristic equations for topological invariants: Pontryagin and Euler classes

By using the Hamilton-Jacobi [HJ] framework the topological theories associated with Euler and Pontryagin classes are analyzed. We report the construction of a fundamental $HJ$ differential where the characteristic equations and the symmetries of the theory are identified. Moreover, we work in both theories with the same phase space variables and we show that in spite of Pontryagin and Euler classes share the same equations of motion their symmetries are different. In addition, we report all HJ Hamiltonians and we compare our results with other formulations reported in the literature.

math-ph↗

arXiv2019

The Hamilton-Jacobi analysis and Canonical Covariant description for three dimensional Palatini theory plus a Chern-Simons term

By using the Hamilton-Jacobi [HJ] framework the three dimensional Palatini theory plus a Chern-Simons term [PCS] is analyzed. We report the complete set of $HJ$ Hamiltonians and a generalized $HJ$ differential from which all symmetries of the theory are identified. Moreover, we show that in spite of PCS Lagrangian produces Einstein's equations, the generalized $HJ$ brackets depend on a Barbero-Immirzi like parameter. In addition we complete our study by performing a canonical covariant analysis, and we construct a closed and gauge invariant two form that encodes the symplectic geometry of the covariant phase space.

math-ph↗

arXiv2018

Hamilton-Jacobi analysis for three dimensional gravity without dynamics

The Hamilton-Jacobi analysis for gravity without dynamics is performed. We report a detailed analysis where the complete set of Hamilton-Jacobi constraints, the characteristic equations and the gauge transformations of the theory are found. We compare our results with those reported in the literature where alternative approaches are used. In addition, we complete our work by performing the canonical covariant analysis by constructing a gauge invariant symplectic structure, and we find a full consistency between the results obtained from both approaches.

gr-qc↗

arXiv2018

Gauge symmetry and constraints structure in topologically massive AdS gravity: A symplectic viewpoint

By applying the Faddeev-Jackiw symplectic approach we systematically show that both the local gauge symmetry and the constraint structure of topologically massive gravity with a cosmological constant $Λ$, elegantly encoded in the zero-modes of the symplectic matrix, can be identified. Thereafter, via an appropriate partial gauge-fixing procedure, the time gauge, we calculate the quantization bracket structure (generalized Faddeev-Jackiw brackets) for the dynamic variables and confirm that the number of physical degrees of freedom is one. This approach provides an alternative to explore the dynamical content of massive gravity models.

hep-th↗

arXiv2017

Canonical and Symplectic analysis of actions describing linearized gravity

By using the canonical and symplectic approaches an (nonstandard) alternative action describing linearized gravity is studied. We identify the complete set of Dirac's constraints, the counting of physical degrees of freedom is performed and the Dirac brackets are constructed. Furthermore, the symplectic analysis is developed which includes the complete set of Faddeev-Jackiw constraints and a symplectic tensor; from that symplectic matrix we show that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide to each other. With all these results at hand, we prove that the number of physical degrees of freedom are eight, thus, we conclude that the theory does not describe the dynamics of linearized gravity. In addition, we also develop the symplectic analysis of standard linearized gravity and we compare the results for both standard and nonstandard theories. Finally we present some remarks and conclusions.

gr-qc↗

arXiv2017

Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes

The symplectic analysis for the four dimensional Pontryagin and Euler invariants is performed within the Faddeev-Jackiw context. The Faddeev-Jackiw constraints and the generalized Faddeev-Jackiw brackets are reported; we show that in spite of the Pontryagin and Euler classes give rise the same equations of motion, its respective symplectic structures are different to each other. In addition, a quantum state that solves the Faddeev-Jackiw constraints is found, and we show that the quantum states for these invariants are different to each other. Finally, we present some remarks and conclusions.

hep-th↗