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arXiv subjects

Josep Llosa

Publications and source records attributed to Josep Llosa.

At least 19 recordsLinked to original sources
arXiv2025

Nonlocal Mechanics

We introduce a Hamiltonian framework for nonlocal Lagrangian systems without relying on infinite-derivative expansions. Starting from a (trajectory-based) variational principle and a generalized Noether theorem, we define the canonical momenta and energy. Moreover, we construct a (pre)symplectic form on the kinematic space, and show that its restriction to the phase space (by implementing the constraints) yields a true (pre)symplectic structure encoding the dynamics. Three examples -- a finite nonlocal oscillator, the fully nonlocal Pais-Uhlenbeck model, and a delayed harmonic oscillator -- demonstrate how phase space and the Hamiltonian emerge without explicitly solving the Euler-Lagrange equations.

hep-th↗
arXiv2025

Are nonlocal Lagrangian systems fatally unstable?

We prove that higher-derivative and genuinely nonlocal Lagrangian systems can be Lyapunov-stable even when their Hamiltonians lack a lower bound. Explicit free and coupled Pais-Uhlenbeck oscillators, together with a genuine nonlocal model, are analysed to identify the precise conditions under which stability holds. These counterexamples point out the logical gap in the "Ostrogradsky instability" claims and provide benchmarks for constructing efficient stable higher-derivative theories.

hep-th↗
arXiv2024

Causality and dielectric functions for linear media with spatial dispersion

We extend Kramers-Kronig relations beyond the optical approximation to dielectric functions that depend not only on frequency but on the wave number as well. This implies extending the notion of causality commonly used in the theory of Kramers-Kronig relations to include the fact that signals cannot propagate faster than light in vacuo. The extension is applied to some microscopic models for the dielectric function and is compared with previous generalizations. The results derived here also apply to general theories of isotropic linear response in which the response function depends on both wave number and frequency.

physics.class-ph↗
arXiv2024

Infinite Derivatives vs Integral Operators. The Moeller-Zwiebach Puzzle

We study the relationship between integral and infinite-derivative operators. In particular, we examine the operator $p^{\frac12\,\partial_t^2}\,$ that appears in the theory of $p$-adic string fields, as well as the Moyal product that arises in non-commutative theories. We also attempt to clarify the apparent paradox presented by Moeller and Zwiebach, which highlights the discrepancy between them.

hep-th↗
arXiv2024

Nonlocal Lagrangian fields and the second Noether theorem. Non-commutative $U(1)$ gauge theory

This article focuses on three main contributions. Firstly, we provide an in-depth overview of the nonlocal Lagrangian formalism. Secondly, we introduce an extended version of the second Noether's theorem tailored for nonlocal Lagrangians. Finally, we apply both the formalism and the extended theorem to the context of non-commutative U(1) gauge theory, including its Hamiltonian and quantization, showcasing their practical utility.

hep-th↗
arXiv2022

Non-local Lagrangian fields: Noether's theorem and Hamiltonian formalism

This article aims to study non-local Lagrangians with an infinite number of degrees of freedom. We obtain an extension of Noether's theorem and Noether's identities for such Lagrangians. We then set up a Hamiltonian formalism for them. In addition, we show that $n$-order local Lagrangians can be treated as a particular case and the standard results can be recovered. Finally, this formalism is applied to the case of $p$-adic open string field.

hep-th↗
arXiv2021

Infinite-derivative linearized gravity in convolutional form

This article aims to transform the infinite-order Lagrangian density for ghost-free infinite-derivative linearized gravity into non-local. To achieve it, we use the theory of generalized functions and the Fourier transform in the space of tempered distributions $\mathcal{S}^\prime$. We show that the non-local operator domain is not defined on the whole functional space but on a subset of it. Moreover, we prove that these functions and their derivatives are bounded in all $\mathbb{R}^3$ and, consequently, the Riemann tensor is regular and the scalar curvature invariants do not present any spacetime singularity. Finally, we explore what conditions we need to satisfy so that the solutions of the linearized equations of motion exist in $\mathcal{S}^\prime$.

gr-qc↗
arXiv2021

Non-local Lagrangian Mechanics: Noether theorem and Hamiltonian formalism

We study Lagrangian systems with a finite number of degrees of freedom that are non-local in time. We obtain an extension of Noether theorem and Noether identities to this kind of Lagrangians. A Hamiltonian formalism is then set up for this systems. $n$-order local Lagrangians can be treated as a particular case and the standard results for them are recovered. The method is then applied to several other cases, namely two examples of non-local oscillators and the p-adic particle.

hep-th↗
arXiv2021

Energy-momentum tensor for the electromagnetic field in a dispersive medium as an application of Noether theorem

On the basis of a non-local Lagrangian for Maxwell equations in a dispersive medium, the energy-momentum tensor of the field is derived. We obtain the Field equations through variational methods and an extension of Noether theorem for a non-local Lagrangian is obtained as well. The electromagnetic energy-momentum tensor obtained in the general context is then specialized to the case of a field with slowly varying amplitude on a rapidly oscillating carrier.

physics.class-ph↗
arXiv2017

Einstein's accelerated reference systems and Fermi-Walker coordinates

We show that the uniformly accelerated reference systems proposed by Einstein when introducing acceleration in the theory of relativity are Fermi-Walker coordinate systems. We then consider more general accelerated motions and, on the one hand we obtain Thomas precession and, on the other, we prove that the only accelerated reference systems that at any time admit an instantaneously comoving inertial system belong necessarily to the Fermi-Walker class.

physics.class-ph↗
arXiv2017

An extension of Poincaré group based on generalized Fermi-Walker coordinates

The class of accelerated and rotating reference frames has been studied on the basis of generalized Fermi-Walker coordinates. We obtain the infinitesimal transformations connecting any two of these frames and also their commutation relations. We thus have an infinite dimensional extension of the Poincaré algebra and, although it turns out to be Abelian extension, and hence trivial, it is noteworthy that, contrarily to Lorentz boosts, acceleration and rotational boost generators commute with each other and with the generators of Poincaré group as well.

gr-qc↗
arXiv2015

An extension of Poincaré group abiding arbitrary acceleration

The class of accelerated reference frames has been studied, on the basis of Fermi-Walker coordinates. The infinitesimal transformations connecting two of these frames has been obtained, and also their commutation relations. The outcome is an infinite dimensional extension of the Poincaré algebra. Although this extension turns out to be Abelian, and hence trivial, it is noteworthy that, contrarily to what happens with Lorentz boosts, acceleration boost generators commute with each other and with translation generators.

gr-qc↗
arXiv2015

An extension of the principle of relativity for one-dimensional space

The class of accelerated reference frames has been studied, on the basis of Fermi-Walker coordinates; both in the cases of uniform and arbitrary accelerations. In the first case, explicit formulae for the transformation of coordinates have been derived and, in both cases, we have also obtained the infinitesimal generators and their commutation relations. The outcome has been an extension of the Poincaré algebra (in 1+1 dimensions), which is infinite dimensional in the case of general acceleration. This extension turns out to be trivial, in the sense that it is Abelian.

gr-qc↗
arXiv2013

Matter and Ricci collineations

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra but also, in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra.

gr-qc↗
arXiv2010

Flat deformation of a spacetime admitting two Killing fields

It is shown that given an analytic Lorentzian metric on a 4-manifold, $g$, which admits two Killing vector fields, then it exists a local deformation law $η= a g + b H$, where $H$ is a 2-dimensional projector, such that $η$ is flat and admits the same Killing vectors. We also characterize the particular case when the projector $H$ coincides with the quotient metric. We apply some of our results to general stationary axisymmetric spacetimes

gr-qc↗
arXiv2009

Flat deformation theorem and symmetries in spacetime

The \emph{flat deformation theorem} states that given a semi-Riemannian analytic metric $g$ on a manifold, locally there always exists a two-form $F$, a scalar function $c$, and an arbitrarily prescribed scalar constraint depending on the point $x$ of the manifold and on $F$ and $c$, say $Ψ(c, F, x)=0$, such that the \emph{deformed metric} $η= cg -εF^2$ is semi-Riemannian and flat. In this paper we first show that the above result implies that every (Lorentzian analytic) metric $g$ may be written in the \emph{extended Kerr-Schild form}, namely $η_{ab} := a g_{ab} - 2 b k_{(a} l_{b)}$ where $η$ is flat and $k_a, l_a$ are two null covectors such that $k_a l^a= -1$; next we show how the symmetries of $g$ are connected to those of $η$, more precisely; we show that if the original metric $g$ admits a Conformal Killing vector (including Killing vectors and homotheties), then the deformation may be carried out in a way such that the flat deformed metric $η$ `inherits' that symmetry.

gr-qc↗