arXiv subjects

Omar Rodríguez-Tzompantzi

Publications and source records attributed to Omar Rodríguez-Tzompantzi.

12 recordsLinked to original sources

arXiv2026

Reducible first-class constraints, gauge symmetry, and the degrees of freedom of three-dimensional gravity coupled to topological matter

We develop a systematic Hamiltonian formulation for a gravitating topological matter system in three-dimensional spacetime, coupling a scalar matter field and a two-form gauge field to first-order Hilbert--Palatini gravity. We perform the Dirac--Bergmann analysis, obtaining the full structure of the constraints, classifying them into first- and second-class ones, and computing their Poisson bracket algebra. Furthermore, we write down the explicit expression for the Hamiltonian generator of gauge symmetries on the full set of canonical variables, containing the exact number of gauge parameters. A mapping of these parameters then shows that the gauge transformations reproduce on-shell the spacetime diffeomorphism and local Poincaré symmetries. The symmetry structure of the coupled model is thereby established on a Cauchy surface without boundary. Our canonical analysis further shows that the first-class constraints obey three reducibility conditions. We trace them back to an off-shell identity of Ricci type and to the redundancy of the gauge parameters carried by the two-form field. In the extended phase-space they close only modulo the second-class sector. Once they are taken into account, the model carries no local degrees of freedom. The fundamental symplectic structure on the reduced phase-space is fixed by the explicit computation of the Dirac brackets. Both these and the Hamiltonian gauge generator are obtained in the extended phase-space, with no canonical variable eliminated beforehand. Finally, we show that on a surface with boundary the improved generator built from the reducible parameters collapses to a single boundary integral, which vanishes identically.

hep-th↗

arXiv2026

Constrained Hamiltonian dynamics of 3D gravity coupled to topological matter

We present the Dirac Hamiltonian formalism for a pair of $1$-form fields with a topological-like potential coupled to first-order gravity in three-dimensional spacetime. By considering the complete phase space, we derive the full structure of the physical constraints, including both primary and secondary ones; analyze their consistency conditions; classify them into first- and second-class; and compute their Poisson-bracket algebra. Our analysis confirms the absence of local degrees of freedom, consistent with the topological nature of the model's action. Furthermore, we construct the canonical generator for gauge transformations and demonstrate that, through appropriate gauge parameter mappings, these transformations recover the full diffeomorphism and Poincaré symmetries of the Lagrangian formulation. Finally, we explicitly compute the Dirac brackets, establishing the symplectic structure of the reduced phase space.

hep-th↗

arXiv2024

Faddeev-Jackiw Hamiltonian formulation for general exotic bi-gravity

General exotic bi-gravity, obtained in Ozkan et al. (Phys Rev Lett 123(3):031303, 2019), is a unitary parity-preserving model which describes two interacting spin-two fields in three-dimensional spacetime. Adopting a symplectic viewpoint, we investigate the dynamical structure of general exotic bi-gravity theory. In particular, by exploiting the properties of the corresponding pre-symplectic matrix and its associated zero-modes, we explicitly derive all constraints of the theory, including the integrability conditions and scalar relationships between all the parameters and fields defining the model. Then, as an application, these scalar relationships are used for studying the anti-de Sitter background. After that, we derive the gauge transformations for the dynamical variables from the structure of the remaining zero-modes, meaning that such zero-modes are indeed the generators of the gauge symmetry of the theory. Finally, by switching off one of the four coupling constants $β_{n}$ and assuming the invertibility of some of the dreibeins, we find that the general exotic bi-gravity theory has two physical degrees of freedom.

hep-th↗

arXiv2022

Canonical description of Exotic General Massive Gravity

Exotic General Massive Gravity is the next-to-simplest gravitational theory fulfilling the so-called third-way consistency, the simplest being Minimal Massive Gravity. We investigate the canonical structure of the first-order formulation of Exotic General Massive Gravity. By using the Dirac Hamiltonian formalism, we systematically discover the complete set of physical constraints, including primary, secondary, and tertiary ones, and explicitly compute the Poisson bracket algebra between them. In particular, we demonstrate that the consistency condition for the tertiary constraints provides explicit expressions which can be solved algebraically for the auxiliary fields $f$ and $h$ in terms of the dreibein $e$. In this configuration, to confirm that the theory is ghost-free, the whole set of constraints is classified into first and second-class ones showing the existence of only two physical degrees of freedom corresponding to one massive graviton. Furthermore, we identify the transformation laws for all of the dynamical variables corresponding essentially to gauge symmetries, generated by the first-class constraints. Finally, by taking into account all the second-class constraints, we explicitly compute the Dirac matrix together with the Dirac's brackets.

hep-th↗

arXiv2021

Conserved laws and dynamical structure of axions coupled to photons

In this work, we carry out a study of the conserved quantities and dynamical structure of the four-dimensional modified axion electrodynamics theory described by the axion-photon coupling. In the first part of the analysis, we employ the covariant phase space method to construct the conserved currents and to derive the Noether charges associated with the gauge symmetry of the theory. We further derive the improved energy-momentum tensor using the Belinfante-Rosenfeld procedure, which leads us to the expressions for the energy, momentum, and energy flux densities. Thereafter, with the help of Faddeev-Jackiw's Hamiltonian reduction formalism, we obtain the relevant fundamental brackets structure for the dynamic variables and the functional measure for determining the quantum transition amplitude. We also confirm that modified axion electrodynamics has three physical degrees of freedom per space point. Moreover, using this symplectic framework, we yield the gauge transformations and the structure of the constraints directly from the zero-modes of the corresponding presymplectic matrix.

hep-th↗

arXiv2021

Symplectic realization of two interacting spin-two fields in three dimensions

We constructed a symplectic realization of the dynamic structure of two interacting spin-two fields in three dimensions. A significant simplification refers to the treatment of constraints: instead of performing a Hamiltonian analysis $\grave{a}\, la$ Dirac, we worked out a method that only uses properties of the pre-symplectic two-form matrix and its corresponding zero-modes to investigate the nature of constraints and the gauge structure of the theory. For instance, we demonstrate that the contraction of the zero-modes with the potential gradient, yields explicit expressions for the whole set of constraints on the dynamics of the theory, including the symmetrization condition and an explicit relationship between the coupling and cosmological constants. This way, we further identify the necessary conditions for the existence of a unique non-linear candidate for a partially massless theory, using only the expression for the interaction parameters of the model. In the case of gauge structure, the transformation laws for the entire set of dynamical variables are more straightforwardly derived from the structure of the remaining zero-modes; in this sense, the zero-modes must be viewed as the generators of the corresponding gauge transformations. Thereafter, we use an appropriate gauge-fixing procedure, the time gauge, to compute both the quantization brackets and the functional measure on the path integral associated with our model. Finally, we confirm that three-dimensional bi-gravity has two physical degrees of freedom per space point. With the above, we provide a new perspective for a better understanding of the dynamical structure of theories of interacting spin-two fields, which does not require the constraints to be catalogued as first- and second-class ones as in the case of Dirac's standard method.

hep-th↗

arXiv2019

Magnetoelectric effect of a conducting sphere near a planar topological insulator

When time-reversal symmetry is broken on its surface, topological insulators exhibit a magnetoelectric response which is described by axion electrodynamics. A direct consequence of this theory is the appearance of a magnetic field that resembles the one produced by a magnetic image monopole when a point-like electric charge is located near the surface of the material. In this paper we investigate the more realistic problem when the point-like charge is replaced by a finite size sphere at constant potential. We calculate the electromagnetic fields using the potential formulation in a particular bispherical coordinate system. We find that the electromagnetic fields can be interpreted in terms of point electric and image magnetic charges as if the medium were the vacuum. As a manifestation of the magnetoelectric effect, we highlight the resulting magnetic field, which we analyze in detail along the symmetry axis, since such estimates could be useful in evaluating the experimental possibility of its measurement via sensible magnetometers. Our numerical estimates show that the proposed setup provides a magnetic field strength in the range of 10-100 mG, which is attainable with present day sensitivities in NV center-diamond magnetometers, for example.

cond-mat.mes-hall↗

arXiv2019

Reversed electromagnetic Vavilov-Čerenkov radiation in naturally existing magnetoelectric media

We consider two semi-infinite magnetoelecteric media separated by a planar interface whose electromagnetic response is described by axion-electrodynamics. The time dependent Green's function characterizing this geometry is obtained by a method which can be directly generalized to cylindrical and spherical configurations of two magnetoelectrics separated by an interface. We establish the far-field approximation of the Green's function and apply these results to the case of a charged particle moving from one medium to the other at a high constant velocity perpendicular to the interface. From the resulting angular distribution of the radiated energy per unit frequency we provide theoretical evidence for the emergence of reversed Vavilov-Čerenkov radiation in naturally existing magnetoelectric media. In the case where one of the magnetolectrics is a 3D topological insulator, ${\rm TlBiSe}_2$ for example, located in front of a regular insulator, we estimate that an average forward Vavilov-Čerenkov radiation with frequency $\sim 2.5 \,\, {\rm eV}$ ($\sim 500\,\, {\rm nm}$) will produce a highly suppressed reversed Vavilov-Čerenkov radiation which can be characterized by an effective frequency in the range of $\sim (4\times 10^{-3}-0.5) \,\, {\rm meV}$. However, this value compares favorably with recent measurements in left-handed metamaterials yielding reversed Vavilov-Čerenkov radiation with frequencies of the order of $(1.2-3.9)\times 10^{-2}\,\, {\rm meV}$.

cond-mat.mes-hall↗

arXiv2019

Explicit spacetime symmetry breaking in matter: the reversed Vavilov-Čerenkov radiation

We show that reversed Vavilov-Čerenkov radiation occurs simultaneously with the forward output in naturally existing materials when an electric charge moves with a constant velocity perpendicular to the planar interface between two magnetoelectric media. Using the Green's function in the far-field approximation we calculate the angular distribution of the radiated energy per unit frequency obtaining a non-zero contribution in the backward direction.

hep-ph↗

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↗

arXiv2018

Constrained dynamics of two interacting relativistic particles in the Faddeev-Jackiw symplectic framework

The Faddeev-Jackiw symplectic formalism for constrained systems is applied to analyze the dynamical content of a model describing two massive relativistic particles with interaction, which can also be interpreted as a bigravity model in one dimension. We systematically investigate the nature of the physical constraints, for which we also determine the zero-modes structure of the corresponding symplectic matrix. After identifying the whole set of constraints, we find out the transformation laws for all the set of dynamical variables corresponding to gauge symmetries, encoded in the remaining zero-modes. In addition, we use an appropriate gauge-fixing procedure, the conformal gauge, to compute the quantization brackets (Faddeev-Jackiw brackets) and also obtain the number of physical degree of freedom. Finally, we argue that this symplectic approach can be helpful for assessing physical constraints and understanding the gauge structure of theories of interacting spin-2 fields.

hep-th↗

arXiv2015

Dirac's and Generalized Faddeev-Jackiw brackets for Einstein's theory in G $\rightarrow 0$ limit

In this paper the Dirac and Faddeev-Jackiw formulation for Einstein's theory in the $G \rightarrow 0$ limit is performed; the fundamental Dirac's and Faddeev-Jackiw brackets for the theory are obtained. First, the Dirac brackets are constructed by eliminating the second class constraints remaining the first class ones, then we fix the gauge and we convert the first class constraints into second class constraints and the new fundamental Dirac's brackets are computed. Alternatively, we reproduce all relevant Dirac's results by means of the symplectic method. We identify the Faddeev-Jackiw constraints and we prove that the Dirac and the Faddeev-Jackiw brackets coincide to each other. .

gr-qc↗