arXiv subjects

H. García-Compeán

Publications and source records attributed to H. García-Compeán.

At least 19 recordsLinked to original sources

arXiv2026

Star-exponential for Fermi systems and the Feynman-Kac formula

Inspired by the formalism that relates the star-exponential with the quantum propagator for bosonic systems, in this work we introduce the analogous extension for the fermionic case. In particular, we analyse the problem of calculating the star-exponential (i.e., the symbol of the evolution operator) for Fermi systems within the deformation quantization program. Grassmann variables and coherent states are considered in order to obtain a closed-form expression for the fermionic star-exponential in terms of its associated propagator. As a primary application, a fermionic version of the Feynman-Kac formula is derived within this formalism, thus allowing a straightforward calculation of the ground state energy in phase space. Finally, the method is validated by successfully applying it to the simple harmonic and driven Fermi oscillators, for which the results developed here provide a powerful alternative computational tool for the study of fermionic systems.

quant-ph↗

arXiv2026

Lorentzian Vacuum Transitions in $f(R)$ gravity

We study Lorentzian vacuum transition probabilities between two minima of a scalar field potential within the framework of $f(R)$ gravity. The analysis extends the previously considered WKB expansion of the Wheeler-DeWitt equation to modified gravity theories, up to second order. We apply the general method for homogeneous and isotropic FLRW universes, with zero and positive spatial curvature, for any $f(R)$ model. For the flat case we obtain analytic expressions for the transition probabilities for any model if we assume a constant Ricci scalar; this assumption has been considered in previous studies, in the Euclidean approach, from symmetry arguments. On the other hand, we also obtain explicit solutions without this assumption for power-law $f(R)=R^{1+n}$ models. Moreover, in the positive curvature scenario, we obtain that the assumption of a constant Ricci scalar is not consistent, but we are able to find analytical solutions in approximated regimes. In all cases we have found that the general behavior of the probabilities already found for Einstein Gravity is preserved, including the prediction of a non-singular initial state due to quantum corrections, even though the probabilities increase or decrease in a model dependent way.

gr-qc↗

arXiv2024

Effects of quantum corrections to Lorentzian vacuum transitions in the presence of gravity

We present a study of the vacuum transition probabilities taking into account quantum corrections. We first introduce a general method that expands previous works employing the Lorentzian formalism of the Wheeler-De Witt equation by considering higher order terms in the semiclassical expansion. The method presented is applicable in principle to any model in the minisuperspace and up to any desired order in the quantum correction terms. Then, we apply this method to obtain analytical solutions for the probabilities up to second quantum corrections for homogeneous isotropic and anisotropic universes. We use the Friedmann-Lemaitre-Robertson-Walker metric with positive and zero curvature for the isotropic case and the Bianchi III and Kantowski-Sachs metrics for the anisotropic case. Interpreting the results as distribution probabilities of creating universes by vacuum decay with a given size, we found that the general behaviour is that considering up to the second quantum correction leads to an avoidance of the initial singularity. However, we show that this result can only be achieved for the isotropic universe. Furthermore, we also study the effect of anisotropy on the transition probabilities.

gr-qc↗

arXiv2024

Hyper-Hermitian Weyl Double Copy

The self-dual double copy is further explored. In previous work, it has been shown that hyper-Hermitian manifolds also have associated the self-dual gauge theories via Kerr-Schild double copy. The self-dual double copy is generalized in the structure of the kinematic algebra by replacing the area-preserving diffeomorphisms algebra with the diffeomorphisms on a surface algebra. This gave rise to the hyper-Hermitian double copy in the Kerr-Schild approach. In the present article, we further study the hyper-Hermitian case using the Weyl double copy formalism. In particular, we have found solutions within this formalism for different hyper-Hermitian metrics. One of the main features is that there will be two Maxwell spinors and one of them is source-free while the other has a source current. This is compatible with the fact that, in general, the hyper-Hermitian spaces are not Ricci-flat.

hep-th↗

arXiv2024

Further Remarks on the Entanglement Entropy of Hopf links

We study the connected sum of Hopf links in $S^3$. Particularly, we compute the entanglement entropy (EE) as a function of the number of link components. We find evidence of lower and upper bounds for the entanglement entropy. We show that the $SU(2)$ theory exhibits sensitivity to the parity of links. We also find evidence suggesting the existence of a well-defined limit of the large number of link components.

hep-th↗

arXiv2024

Classical Kerr-Schild double copy in bigravity for maximally symmetric spacetimes

A generalized Kerr-Schild ansatz for bigravity, already considered in the literature, which leads to linear interactions between the metrics is used to study the bigravity equations in the context of the double copy. By contracting the resulting spin-2 field bigravity equations of motion using Killing vector fields, as is usually carried out in general relativity, we arrive to the single and zeroth copy equations for the mentioned ansatz. For the case of stationary solutions, we obtain two Maxwell and two conformally coupled scalar field equations for the single and zeroth copies respectively, and the linear interactions are absent. In the time-dependent case we obtain equations for the fields which are coupled. By decoupling these equations and at the zeroth copy level, we recover a massless and a massive field whose mass is proportional to the Fierz-Pauli mass and depends on the coefficients of the interaction potential between the metrics. This has been also previously documented in the literature and is now reinterpreted within the context of the double copy proposal.

gr-qc↗

arXiv2023

Dyonic black holes: The theory of two electromagnetic potentials

In the present paper we argue that the dyonic black hole spacetimes must be studied within the theory of two electromagnetic potentials, and we use the dyonic Reissner-Nordström solution to demonstrate that the field of the monopole magnetic charge is correctly described by the $t$-component of the dual electromagnetic potential. As a result, the Dirac string associated with the $φ$-component of the usual electromagnetic 4-potential becomes just a mathematical object, without any physical content, that arises in some calculations when one employs unsymmetrical representations of the electromagnetic field. We use three different, though equivalent, forms of the electromagnetic energy-momentum tensor to calculate the Komar mass of the Reissner-Nordström black hole, and in one case the Dirac string is linked to the magnetic charge, in another to the electric charge, while the third, symmetrical case, is string-free.

gr-qc↗

arXiv2023

Dyonic black holes: The theory of two electromagnetic potentials. II

The results obtained in our previous paper are now extended to the case of stationary axially symmetric dyonic black boles within the theory of two electromagnetic potentials. We slightly enlarge the classical Ernst formalism by introducing, with the aid of the $t$- and $φ$-components of the dual potential $B_μ$, the magnetic potential $Φ_m$ which, similar to the known electric potential $Φ_e$, also takes constant value on the black hole horizon. We analyze in detail the case of the dyonic Kerr-Newman black hole and show how the Komar mass must be evaluated correctly in this stationary dyonic model. In particular, we rigorously prove the validity of the standard Tomimatsu mass formula and point out that attempts to "improve" it made in recent years are explained by misunderstanding of the auxiliary role that singular potentials play in the description of magnetic charges. Our approach is symmetrical with respect to electric and magnetic charges and, like in the static case considered earlier, Dirac strings of all kind are excluded from the physical picture of the stationary black hole dyonic spacetimes.

gr-qc↗

arXiv2022

Euclidean Quantum Field Formulation of p-Adic open string amplitudes

We study in a rigorous mathematical way p-adic quantum field theories whose N-point amplitudes are the expectation of products of vertex operators. We show that this type of amplitudes admit a series expansion where each term is an Igusa's local zeta function. The lowest term in this series is a regularized version of the p-adic open Koba-Nielsen string amplitude.

hep-th↗

arXiv2021

Lorentzian Vacuum Transitions for Anisotropic Universes

The vacuum transition probabilities for anisotropic universes in the presence of a scalar field potential in the Wentzel-Kramers-Brillouin approximation are studied. We follow the work by Cespedes et al [Phys. Rev. D 104, 026013 (2021)], which discuss these transitions in the isotropic context using the Wheeler-DeWitt equation, the Lorentzian Hamiltonian approach and the thin wall limit. First, we propose a general procedure to adapt their formalism to compute the decay rates for any superspace model. Then we apply it to compute the transition probabilities of an Friedmann-Lemaitre-Robertson-Walker (FLRW) metric with both positive and zero curvature, reproducing in this way one of the results obtained at Cespedes et al. We then proceed to apply the formalism to three anisotropic metrics, namely, Kantowski-Sachs, Bianchi III and biaxial Bianchi IX to compute the rate decays for these three cases. In the process we find that this method involves some conditions which relates the effective number of independent degrees of freedom resulting on all probabilities being described with only two independent variables. For the Bianchi III metric, we find that a general effect of anisotropy is to decrease the transition probability as the degree of anisotropy is increased, having as the isotropic limit the flat FLRW result.

hep-th↗

arXiv2021

The temperature and free energy of multi-black hole systems

In the present paper, we compute the Euclidean action of a generic system consisting of $N$ arbitrary Kerr-Newman black holes located on the symmetry axis and separated from each other by massless struts. This allows us to introduce the {\it Hawking average temperature} (HAT) $\hat T$ of the multi-black hole system via the condition of vanishing the entire set of terms involving the singular horizons due to periodic time, and the resulting formula for this temperature contains solely the surface gravities $κ_i$ and horizon areas $A^H_i$ of the black hole constituents. We also show that the corresponding expression for the {\it free energy} of the system defined by $\hat T$ is consistent with the first law of thermodynamics and Smarr mass relations.

gr-qc↗

arXiv2021

Local Zeta Functions and Koba-Nielsen String Amplitudes

This article is a survey of our recent work on the connections between Koba-Nielsen amplitudes and local zeta functions (in the sense of Gel'fand, Weil, Igusa, Sato, Bernstein, Denef, Loeser, etc.). Our research program is motivated by the fact that the p-adic strings seem to be related in some interesting ways with ordinary strings. For instance, connections through the adelic relations and through the limit when p tends to 1. Gerasimov and Shatashvili studied the limit p tends to 1 of the p-adic effective action introduced by Brekke, Freund, Olson and Witten. They showed that this limit gives rise to a boundary string field theory, which was previously proposed by Witten in the context of background independent string theory. Explicit computations in the cases of 4 and 5 points show that the Feynman amplitudes at the tree level of the Gerasimov-Shatashvili Lagrangian are related with the limit p tends to 1 of the p-adic Koba-Nielsen amplitudes. At a mathematical level, this phenomenon is deeply connected with the topological zeta functions introduced by Denef and Loeser. A Koba-Nielsen amplitude is just a new type of local zeta function, which can be studied by using embedded resolution of singularities. In this way, one shows the existence of a meromorphic continuations for the Koba-Nielsen amplitudes as functions of the kinematic parameters. The Koba-Nielsen local zeta functions are algebraic-geometric integrals that can be defined over arbitrary local fields (for instance R, C, Q_{p}, F_{p}((T)), and it is completely natural to expect connections between these objects. The limit p tends to one of the Koba-Nielsen amplitudes give rise to a new amplitudes which we have called Denef-Loeser amplitudes. Along the article, we have emphasized the explicit calculations in the cases of 4 and 5 points.

hep-th↗

arXiv2021

On $2k$-Hitchin's equations and Higgs bundles: a survey

We study the $2k$-Hitchin equations introduced by Ward \cite{Ward 2} from the geometric viewpoint of Higgs bundles. After an introduction on Higgs bundles and $2k$-Hitchin's equations, we review some elementary facts on complex geometry and Yang-Mills theory. Then we study some properties of holomorphic vector bundles and Higgs bundles and we review the Hermite-Yang-Mills equations together with two functionals related to such equations. Using some geometric tools we show that, as far as Higgs bundles is concern, $2k$-Hitchin's equations are reduced to a set of two equations. Finally, we introduce a functional closely related to $2k$-Hitchin's equations and we study some of its basic properties.

math.DG↗

arXiv2020

Star-triangle type relations from $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ dualities

Inspired by the gauge/YBE correspondence this paper derives some star-triangle type relations from dualities in $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ supersymmetric quiver gauge theories. To be precise, we study two cases. The first case is the Intriligator-Pouliot duality in $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ theories. The description is performed explicitly for $N=1,2,3,4,5$ and also for $N=3k+2$, which generalizes the situation in $N=2,5$. For $N=1$ a triangle identity is obtained. For $N=2,5$ it is found that the realization of duality implies slight variations of a star-triangle relation type (STR type). The values $N=3,4$ are associated to a similar version of the asymmetric STR. The second case is a new duality for $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ theories with matter in the antisymmetric tensor representation that arises from dimensional reduction of $4d$ $\mathcal{N}=1$ $USp(2N)$ Csáki-Skiba-Schmaltz duality. It is shown that this duality is associated to a triangle type identity for any value of $N$. In all cases Boltzmann weights as well as interaction and normalization factors are completely determined. Finally, our relations are compared with those previously reported in the literature.

hep-th↗

arXiv2020

Thermodynamics of two aligned Kerr-Newman black holes

Using the notion of thermodynamic length, the first law of thermodynamics is consistently derived for two binary configurations of equal Kerr-Newman black holes separated by a massless strut. Like in the electrostatic systems of two Reissner-Nordström black holes and stationary vacuum systems of two Kerr black holes considered earlier, the thermodynamic length $\ell$ turns out to be defined by the same simple formula $\ell=L\exp(γ_0)$, $L$ being the coordinate length of the strut and $γ_0$ the value of the metric function $γ$ on the strut, which permits the elaboration of $\ell$ in a concise analytic form. The expression of the free energy in the case of two generic Kerr-Newman black holes is also proposed.

gr-qc↗

arXiv2020

Thermodynamics of two aligned Kerr black holes

We investigate the first law of thermodynamics in the stationary axisymmetric configurations composed of two Kerr black holes separated by a massless strut. Our analysis employs the recent results obtained for the extended double-Kerr solution and for thermodynamics of the static single and binary black holes. We show that, similar to the electrostatic case, in the stationary binary systems the thermodynamic length $\ell$ is defined by the formula $\ell=L\exp(γ_0)$, where $L$ is the coordinate length of the strut, and $γ_0$ is the value of the metric function $γ$ on the strut.

gr-qc↗

arXiv2020

Comments on two papers of Clément and Gal'tsov

We comment on physical inconsistences of the Clément-Gal'tsov approach to Smarr's mass formula in the presence of magnetic charge. We also point out that the results of Clément and Gal'tsov involving the NUT parameter are essentially based on the known study (dating back to 2006) of the Demiański-Newman solutions which was not cited by them.

gr-qc↗

arXiv2020

Vassiliev Invariants for Flows Via Chern-Simons Perturbation Theory

The perturbative expansion of Chern-Simons gauge theory leads to invariants of knots and links, the finite type invariants or Vassiliev invariants. It has been proven that at any order in perturbation theory the resulting expression is an invariant of that order. Bott-Taubes integrals on configuration spaces are introduced in the present context to write Feynman diagrams at a given order in perturbation theory in a geometrical and topological setting. One of the consequences of the configuration space formalism is that the resulting amplitudes are given in cohomological terms. This cohomological structure can be used to translate Bott-Taubes integrals into Chern-Simons perturbative amplitudes and vice versa. In this article this program is performed up to third order in the coupling constant. This expands some work previously worked out by Thurston. Finally we take advantage of these results to incorporate in the formalism a smooth and divergenceless vector field on the $3$-manifold. The Bott-Taubes integrals obtained are used for constructing higher-order asymptotic Vassiliev invariants extending the work of Komendarczyk and Volić.

hep-th↗