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E. Huguet

Publications and source records attributed to E. Huguet.

At least 19 recordsLinked to original sources
arXiv2026

FLRW embeddings in $\mathbb{R}^{n+2}$, differential geometry and conformal photon propagator

This paper introduces differential-geometric methods to study $n$-dimensional locally conformally flat spaces as submanifolds in $\mathbb{R}^{n+2}$. We derive explicit formulas relating intrinsic and ambient differential-geometric objects, including curvature tensors, the codifferential and laplacian operators. We apply this approach to Friedmann-Lemaître-Robertson-Walker (FLRW) spaces using newfound embedding formulas, obtaining new and simplified expressions for the photon propagator in four dimensions.

math-ph↗
arXiv2023

Asymptotic states and $S$-matrix operator in de Sitter ambient space formalism

Within the de Sitter ambient space framework, the two different bases of the one-particle Hilbert space of the de Sitter group algebra are presented for the scalar case. Using field operator algebra and its Fock space construction in this formalism, we discuss the existence of asymptotic states in de Sitter QFT under an extension of the adiabatic hypothesis and prove the Fock space completeness theorem for the massive scalar field. We define the quantum state in the limit of future and past infinity on the Sitter hyperboloid in an observer-independent way. These results allow us to examine the existence of the $S$-matrix operator for de Sitter QFT in ambient space formalism, a question usually obscure in spacetime with a cosmological event horizon for a specific observer. Some similarities and differences between QFT in Minkowski and de Sitter spaces are discussed.

hep-th↗
arXiv2022

Restriction of Laplace operator on one-forms: from $\mathbb{R}^{n+2}$ and $\mathbb{R}^{n+1}$ ambient spaces to embedded (A)dS$_n$ submanifolds

The Laplace-de Rham operator acting on a one-form $a$: $\square a$, in $\mathbb{R}^{n+2}$ or $\mathbb{R}^{n+1}$ spaces is restricted to $n$-dimensional pseudo-spheres. This includes, in particular, the $n$-dimensional de Sitter and Anti-de Sitter space-times. The restriction is designed to extract the corresponding $n$-dimensional Laplace-de Rham operator acting on the corresponding $n$-dimensional one-form on pseudo-spheres. Explicit formulas relating these two operators are given in each situation. The converse problem, of extending an $n$-dimensional operator composed of the sum of the Laplace-de Rham operator and additional terms to ambient spaces Laplace-de Rham operator, is also studied. We show that for any additional term this operator on the embedded space is the restriction of Laplace-de Rham operator on the embedding space.These results are translated to the Laplace-Beltrami operator thanks to the Weitzenböck formula, for which a proof is also given.

math-ph↗
arXiv2021

Cartan approach to Teleparallel Equivalent to General Relativity: a review

In previous works, questioning the mathematical nature of the connection in the translations gauge theory formulation of Teleparallel Equivalent to General Relativity (TEGR) Theory led us to propose a new formulation using a Cartan connection. In this review, we summarize the presentation of that proposal and discuss it from a gauge theoretic perspective.

gr-qc↗
arXiv2020

Teleparallel gravity as a gauge theory: coupling to matter with Cartan connection

We present a consistent and complete description of the coupling to matter in the Teleparallel Equivalent to General Relativity (TEGR) theory built from a Cartan connection, as we proposed in previous works. A first theorem allows us to obtain parallel transport from the Cartan connection into a proper Ehresmann connection, while a second ensures to link the TEGR-Cartan connection to the Ehresmann one-form that contains the Levi-Civita connection. This yields a coupling to matter in agreement with observations and the Equivalence Principle. As the fundamental fields proceed from the Cartan connection, if one insists on interpreting TEGR as a gauge theory of translations, such translation gauge field can be extracted from the consistent theory presented. However, this would entail a fundamental change in the structures known for gauge theory and a split between gauge field and connection is imperative. The willingness to take such a step is left to the reader.

gr-qc↗
arXiv2020

Massive scalar field on (A)dS space from a massless conformal field in $\mathbb{R}^6$

We show how the equations for the scalar field (including the massive, massless, minimally and conformally coupled cases) on de Sitter and Anti-de Sitter spaces can be obtained from both the SO$(2,4)$-invariant equation $\square ϕ= 0$ in $\mathbb{R}^6$ and two geometrical constraints defining the (A)dS space. Apart from the equation in $\mathbb{R}^6$, the results only follow from the geometry.

gr-qc↗
arXiv2019

Teleparallel theory as a gauge theory of translations: comments and issues

The Teleparallel Equivalent to General Relativity (TEGR) is often presented as a gauge theory of translations, i.e., that uses \emph{only} the translation group $T_4 = (\setR^4, +)$ as its gauge group. In a previous work we argued against this \emph{translation-only} formalism on the basis of its mathematical shortcomings. We then provided an alternative proposal using a Cartan connection. Recently, a reply by some of the authors defending TEGR as a \emph{translation-only} gauge theory discussed our objections. Here, we first clarify our arguments, and give new proofs of some statements, to answer to these discussions, maintaining our first claim. We then amend one of the argument that originally led us to propose the Cartan connection in this context. This broadens the \emph{a priori} possible choices for a TEGR connection.

gr-qc↗
arXiv2018

Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection?

In this paper we question the status of TEGR, the Teleparallel Equivalent of General Relativity,as a gauge theory of translations. We observe that TEGR (in its usual translation-gauge view) does not seem to realize the generally admitted requirements for a gauge theory for some symmetry group $G$: namely it does not present a mathematical structure underlying the theory which relates to a principal $G$-bundle and the choice of a connection on it (the gauge field). We point out that, while it is usually presented as absent, the gauging of the Lorentz symmetry is actually present in the theory, and that the choice of an Erhesmann connection to describe the gauge field makes the translations difficult to implement (mainly because there is in general no principal translation-bundle). We finally propose to use the Cartan Geometry and the Cartan connection as an alternative approach, naturally arising from the solution of the issues just mentioned, to obtain a more mathematically sound framework for TEGR.

gr-qc↗
arXiv2017

FLRW spaces as submanifolds of $\mathbb{R}^6$: restriction to the Klein-Gordon operator

The FLRW spacetimes can be realized as submanifolds of $\mathbb{R}^6$. In this paper we relate the Laplace-Beltrami operator for an homogeneous scalar field $ϕ$ of $\mathbb{R}^6$ to its explicit restriction on FLRW spacetimes. We then make the link between the homogeneous solutions of the equation $\square_6 ϕ= 0$ in $\mathbb{R}^6$ and those of the Klein-Gordon equation $(\square_{f} - ξR^f + m^2)ϕ^f=0 $ for the free field $ϕ^f$ in the FLRW spacetime. We obtain as a byproduct a formula for the Ricci scalar of the FRLW spacetime in terms of the function $f$ defining this spacetime in $\mathbb{R}^6$.

math-ph↗
arXiv2014

Conformally invariant wave equation for a symmetric second rank tensor ("spin-2") in d-dimensional curved background

We build the general conformally invariant linear wave operator for a free, symmetric, second-rank tensor field in a d-dimensional ($d\geqslant 2$) metric manifold, and explicit the special case of maximally symmetric spaces. Under the assumptions made, this conformally invariant wave operator is unique. The corresponding conformally invariant wave equation can be obtained from a Lagrangian which is explicitly given. We discuss how our result compares to previous works, in particular we hope to clarify the situation between conflicting results.

gr-qc↗
arXiv2013

Conformally invariant formalism for the electromagnetic field with currents in Robertson-Walker spaces

We show that the Laplace-Beltrami equation $\square_6 a =j$ in $(\setR^6,η)$, $η:= \mathrm{diag}(+----+)$, leads under very moderate assumptions to both the Maxwell equations and the conformal Eastwood-Singer gauge condition on conformally flat spaces including the spaces with a Robertson-Walker metric. This result is obtained through a geometric formalism which gives, as byproduct, simplified calculations. In particular, we build an atlas for all the conformally flat spaces considered which allows us to fully exploit the Weyl rescalling to Minkowski space.

gr-qc↗
arXiv2011

Simple fluid models for super-inflation in effective LQC and effects on the CMB B-modes

Loop quantum cosmology allows to replace the original singularity by a quantum bounce followed by a phase of fast expansion called super-inflation. In this paper, we use a simple analytic description of super-inflation using the equation of state of a fluid. We then derive the power spectrum of tensor perturbations produced. The effects on the B-mode polarization of the cosmological background radiation are discussed. For a large region of phase space, the spectrum should be distinguishable from the standard inflationary prediction for future observations.

gr-qc↗
arXiv2011

Conformal use of retarded Green's functions for the Maxwell field in de Sitter space

We propose a new propagation formula for the Maxwell field in de Sitter space which exploit the conformal invariance of this field together with a conformal gauge condition. This formula allows to determine the classical electromagnetic field in the de Sitter space from given currents and initial data. It only uses the Green's function of the massless Minkowskian scalar field. This leads to drastic simplifications in practical calculations. We apply this formula to the classical problem of the two charges of opposite signs at rest at the North and South Poles of the de Sitter space.

gr-qc↗