arXiv subjects

O. Abla

Publications and source records attributed to O. Abla.

4 recordsLinked to original sources

arXiv2026

Conservation laws in classical Poisson field theories

Poisson electrodynamics is the semiclassical limit of the full $U(1)$ non-commutative gauge theory, also known in recent literature as Poisson gauge theory. Two consolidated models for the theory studied in recent years, with a specific choice of non-commutative parameter, Lie-Poisson structures and constant ones, the later also known as the canonical, or Heisenberg case. In this paper, we present the theory considering the new building blocks related to symmetries and conservation laws, as a first step toward understanding the necessary mathematical tools to uncover some of the unknown pieces. We consider non-interacting examples of pure gauge fields, and classical Poisson field theories, related with real and complex scalar fields, as well as fermionic fields, using a constant spacelike deformation parameter. We show that the non-relativistic limit for the non-commutative Dirac equation introduces an orbital Zeeman coupling term for the fermionic fields, and the energy shift in the first excited state depends exclusively on the non-commutative parameter.

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arXiv2024

Poisson electrodynamics on $\kappa$-Minkowski space-time

Poisson electrodynamics is the semi-classical limit of $U(1)$ non-commutative gauge theory. It has been studied so far as a theoretical model, where an external field would be the source of the non-commutative effects in space-time. Being the Standard Model of fundamental interactions a local theory, the prediction of observables within it would be drastically altered by such effects. The natural question that arises is: how do particles interact with this field ? In this work, we will answer this question using point-like charged particles interacting with the Poisson gauge field, investigating how their trajectories are affected using the $\kappa$-Minkowski structure. The interaction arises from the construction of a gauge-invariant action. Using the field solutions, we find the second-order equation for the deformed Lorentz force, indicating possible effects of an emergent gravity due to non-commutativity.

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arXiv2023

Effects of wave propagation in canonical Poisson gauge theory under an external magnetic field

The non-commutative electrodynamics based on the canonical Poisson gauge theory is studied in this paper. For a pure spatial non-commutativity, we investigate the plane wave solutions in the presence of a constant and uniform magnetic background field for the classical electrodynamics in canonical Poisson gauge theory. We obtain the properties of the medium ruled by the permittivity and the permeability tensors in terms of the non-commutative parameter, with the electrodynamics equations in the momentum space. Using the plane wave solutions mentioned, the dispersion relations are modified by the magnetic background, and the correspondent group velocity is affected by the spatial non-commutative parameter. We construct the energy-momentum tensor and discuss the conserved components of this tensor in the spatial non-commutative case. The birefringence phenomenon is showed through the modified dispersion relations, that depends directly on the non-commutative corrections and also on the magnetic background field. Using the bound of the polarized vacuum with laser (PVLAS) experiment for the vacuum magnetic birefringence, we estimate a theoretical value for the spatial non-commutative parameter.

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arXiv2022

On the L$_\infty$ structure of Poisson gauge theory

The Poisson gauge theory is a semi-classical limit of full non-commutative gauge theory. In this work we construct an L$_\infty^{full}$ algebra which governs both the action of gauge symmetries and the dynamics of the Poisson gauge theory. We derive the minimal set of non-vanishing $\ell$-brackets and prove that they satisfy the corresponding homotopy relations. On the one hand, it provides new explicit non-trivial examples of L$_\infty$ algebras. On the other hand, it can be used as a starting point for bootstrapping the full non-commutative gauge theory. The first few brackets of such a theory are constructed explicitly in the text. In addition we show that the derivation properties of $\ell$-brackets on L$_\infty^{full}$ with respect to the truncated product on the exterior algebra are satisfied only for the canonical non-commutativity. In general, L$_\infty^{full}$ does not have a structure of P$_\infty$ algebra.

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