arXiv subjects

José Javier Relancio

Publications and source records attributed to José Javier Relancio.

7 recordsLinked to original sources

arXiv2025

Unified field theory from Hamilton cotangent bundle geometry - The Einstein-Maxwell system

The unification of all physical fields into one mathematical object and the derivation of all physical field equations from that object in one framework is a long-lasting endeavor in fundamental physics. We suggest a new approach to achieve this goal by encoding physical fields into the geometry of the 1-particle phase space on spacetime (the cotangent bundle) through Hamilton geometry. The fundamental field, which contains information about all physical fields in spacetime and defines the phase space geometry, is a scalar field in phase space that is interpreted as a point-particle Hamiltonian. We construct an action principle for scalar fields in phase space and derive the corresponding scalar field equation. By choosing a specific scalar field, namely the Hamiltonian describing a charged particle in curved spacetime with an electromagnetic field, we show that this phase-space scalar field equation is equivalent to the coupled Einstein-Maxwell equations in spacetime, thus providing a geometric unification of gravity and electromagnetism. We further discuss how this approach differs from previous unification attempts and its potential for describing further physical fields and their dynamics in a unified manner in terms of phase-space geometry.

gr-qc↗

arXiv2023

Double Quantization

In a quantum gravity theory, it is expected that the classical notion of spacetime disappears, leading to a quantum structure with new properties. A possible way to take into account these quantum effects is through a noncommutativity of spacetime coordinates. In the literature, there is not a clear way to describe at the same time a noncommutativity of spacetime and the phase-space noncommutativity of quantum mechanics. In this paper we address this issue by constructing a Drinfel'd twist in phase space which deals with both quantizations. This method can be applied to a noncommutativity which involves only space, leaving time aside. We apply our construction to the so-called $λ$-Minkwoski and $\mathbb{R}^3_λ$ noncommutative spaces.

hep-th↗

arXiv2022

Deformed relativistic symmetry principles

We review the main features of models where relativistic symmetries are deformed at the Planck scale. We cover the motivations and links to other quantum gravity approaches. We describe in some detail the most studied theoretical frameworks, including Hopf algebras, relative locality, and other scenarios with deformed momentum space geometry. We discuss possible phenomenological consequences, and point out current open questions.

hep-th↗

arXiv2022

Exploring black holes as particle accelerators: hoop-radius, target particles and escaping conditions

The possibility that rotating black holes could be natural particle accelerators has been subject of intense debate. While it appears that for extremal Kerr black holes arbitrarily high center of mass energies could be achieved, several works pointed out that both theoretical as well as astrophysical arguments would severely dampen the attainable energies. In this work we study particle collisions near Kerr black holes, by reviewing and extending the so far proposed scenarios. Most noticeably, we shall focus on the recently advanced target particle scenarios which were claimed to reach arbitrarily high energies even for Schwarzschild black holes. By implementing the hoop conjecture we show that these scenarios involving near-horizon target particles are in principle able to attain, sub-Planckian, but still ultra-high center of mass energies of the order of $10^{23}-10^{25}$ eV even for non-extremal Kerr black holes. Furthermore, analysing the properties of particles produced in such collisions, we find that photons can escape to infinity. However, their energy is only of the order of the energy of the colliding particles and hence relatively low, which is the same conclusion previously reached in the literature about the original Bañados--Silk--West process. This finding points towards a general limitation of collisional Penrose processes, at least for what concerns their primary products.

gr-qc↗

arXiv2022

Deformed relativistic kinematics on curved spacetime -- a geometric approach

Deformed relativistic kinematics have been considered as a way to capture residual effects of quantum gravity. It has been shown that they can be understood geometrically in terms of a curved momentum space on a flat spacetime. In this article we present a systematic analysis under which conditions and how deformed relativistic kinematics, encoded in a momentum space metric on flat spacetime, can be lifted to curved spacetimes in terms of a self-consistent cotangent bundle geometry, which leads to purely geometric, geodesic motion of freely falling point particles. We comment how this construction is connected to, and offers a new perspective on, non-commutative spacetimes. From geometric consistency conditions we find that momentum space metrics can be consistently lifted to curved spacetimes if they either lead to a dispersion relation which is homogeneous in the momenta, or, if they satisfy a specific symmetry constraint. The latter is relevant for the momentum space metrics encoding the most studied deformed relativistic kinematics. For these, the constraint can only be satisfied in a momentum space basis in which the momentum space metric is invariant under linear local Lorentz transformations. We discuss how this result can be interpreted and the consequences of relaxing some conditions and principles of the construction from which we started.

gr-qc↗

arXiv2021

Particle-antiparticle asymmetry in a relativistic deformed kinematics

Relativistic deformed kinematics are usually considered as a way to capture residual effects of a fundamental quantum gravity theory. These kinematics present a non-commutative addition law for the momenta, so that the total momentum of a multi-particle system depends on the specific ordering in which the momenta are composed. We explore in the present work how this property may be used to generate an asymmetry between particles and antiparticles through a particular ordering prescription, resulting in a violation of CPT symmetry. We study its consequences for muon decay, obtaining a difference in the lifetimes of the particle and the antiparticle as a function the new high-energy scale parameterizing such a relativistic deformed kinematics.

hep-ph↗

arXiv2021

Curved momentum space, locality, and generalized space-time

We establish the correspondence between two apparently unrelated but in fact complementary approaches of a relativistic deformed kinematics: the geometric properties of momentum space and the loss of absolute locality in canonical spacetime, which can be restored with the introduction of a generalized spacetime. This correspondence is made explicit for the case of $κ$-Poincaré kinematics and compared with its properties in the Hopf algebra framework.

gr-qc↗