arXiv subjects

Loïc Marsot

Publications and source records attributed to Loïc Marsot.

8 recordsLinked to original sources

arXiv2026

Statistical Physics of Planar Carroll Systems

In this article, we define and study the statistical physics of planar Carrollian systems. While it has been shown recently that, for general dimensions, the Carroll limit of Poincaré statistical physics typically does not converge, we show that thanks to the central extensions of the Carroll algebra in the plane, and by considering systems with angular momentum, there exists a well defined notion of planar Carrollian statistical physics. Using Souriau's geometric thermodynamics, we compute the partition function for particles on a uniformly rotating disc, and show that rotation is inevitable for thermal equilibrium of planar Carroll systems, with one of the central charges determining the direction of rotation. We derive thermodynamic quantities in particular entropy, which scales logarithmically with the disc area, and pressure, which follows the two-dimensional ideal gas law. Though all results are obtained from symmetry considerations, we also derive the corresponding effective Hamiltonian.

math-ph↗

arXiv2025

Equations of motion for dynamical systems with angular momentum on Finsler geometries

This article aims to derive equations of motion for dynamical systems with angular momentum on Finsler geometries. To this end, we apply Souriau's Principle of General Covariance, which is a geometrical framework to derive diffeomorphism invariant equations of motion. The equations we obtain are the generalization of that of Mathisson-Papapetrou-Dixon (MPD) on Finsler geometries, and we give their conserved quantities which turn out to be formally identical to the Riemannian case. These equations share the same properties as the MPD equations, and we mention different choices possible for supplementary conditions to close this system of equations. These equations have an additional requirement, which is the choice of what defines the tangent direction of the Finsler manifold, since the velocity and momentum are not parallel in general. After choosing the momentum as the Finsler direction and to define the center of mass, we give the complete equations of motion in 3 spatial dimensions, which we find coincide to previously known equations for Finsler spinoptics, and novel equations in 4 dimensions for massive and massless dynamical systems.

math-ph↗

arXiv2023

Induced motions on Carroll geometries

In this article, we consider some Carrollian dynamical systems as effective models on null hypersurfaces in a Lorentzian spacetime. We show that we can realize Carroll models from more usual ``relativistic'' theories. In particular, we show how ambient null geodesics imply the classical ``no Carroll motion'' and, more interestingly, we find that the ambient model of chiral fermions implies Hall motion on null hypersurfaces, in agreement with previous intrinsic Carroll results. We also show how Wigner-Souriau translations imply (apparent) Carroll motion, and how ambient particles with a non vanishing gyromagnetic ratio cannot have a Carrollian description.

gr-qc↗

arXiv2022

Planar Carrollean dynamics, and the Carroll quantum equation

We expand on the known result that the Carroll algebra in $2+1$ dimensions admits two non-trivial central extensions by computing the associated Lie group, which we call extended Carroll group. The symplectic geometry associated to this group is then computed to describe the motion of planar Carroll elementary particles, in the free case, when coupled to an electromagnetic field, and to a gravitational field. We compare to the motions of Carroll particles in $3+1$ dimensions in the same conditions, and also give the dynamics of Carroll particles with spin. In an electromagnetic background, the planar Carroll dynamics differ from the known Carroll ones due to 2 new Casimir invariants, and turn out to be non-trivial. The coupling to a gravitational field leaves the dynamics trivial, however. Finally, we obtain the quantum equation obeyed by Carroll wave functions \textit{via} geometric quantization.

math-ph↗

arXiv2021

Conformal and projective tractors from 2-frame bundles by the dressing field method

This paper is devoted to the study of conformal and projective structures, and especially their connections, in the language of 2-frames, or $G$-structures of 2nd-order. While their normal Cartan connections are well-known, we use the dressing field method to obtain their local, mostly gauge invariant, connections. Lastly, we recall how to obtain the tractor bundle from conformal structures, and then show that we can define a projective tractor bundle using the same kind of construction.

math-ph↗

arXiv2021

Geometric studies of the interplay between spin and gravity

This PhD thesis is the conclusion of some of my works carried out at the Centre de Physique Théorique, under the supervision of Serge Lazzarini. Two subjects are presented in the manuscript, both aiming at studying the effect of the spin of elementary particles on otherwise known theories. First is a study of the Lévy-Leblond-Newton (LLN) equation, which is used to describe the evolution of a quantum system with spin 1/2 that is coupled to its own gravitational potential. After reviewing some symmetries of non relativistic Quantum Mechanics, and how to geometrize them with the help of Bargmann structures, we recall what is the Lévy-Leblond equation. In this chapter, the LLN equation is described in a fully covariant way on Bargmann structures. This covariant formulation then helps to derive the dynamical symmetries of the equation, and conserved quantities. The symmetry group of this equation turns out to be the already known Schrödinger-Newton group. The second part deals with the trajectory of particles with spin in General Relativity. We first highlight Souriau's geometric method to derive the Mathisson-Papapetrou-Dixon (MPD) equations, and then discuss the different possible Spin Supplementary Conditions (SSC) that exist to close the system of MPD equations. In this chapter, we assume the Tulczyjew SSC to describe the trajectory of photons, leading to the Souriau-Saturnini equations. We then present some works where we have applied these equations, in a Schwarzschild spacetime, and in a spacetime deformed by a gravitational wave. In the first work, we found gravitational birefringence: the trajectory deviates from the geodesic plane, depending on the helicity of the photon and its wavelength. The second work presented also found birefringence in gravitational interferometry experiments, however the effect is many orders of magnitude lower than what we can detect.

gr-qc↗

arXiv2019

On the Lévy-Leblond-Newton equation and its symmetries: a geometric view

The Lévy-Leblond-Newton (LLN) equation for non-relativistic fermions with a gravitational self-interaction is reformulated within the framework of a Bargmann structure over a $(n+1)$-dimensional Newton-Cartan (NC) spacetime. The Schrödinger-Newton (SN) group, introduced in [21] as the maximal group of invariance of the SN equation, turns out to be also the group of conformal Bargmann automorphisms preserving the coupled Lévy-Leblond and NC gravitational field equations. Within the Bargmann geometry a generalization of the LLN equation is provided as well. The canonical projective unitary representation of the SN group on 4-component spinors is also presented. In particular, when restricted to dilations, the value of the dynamical exponent $z=(n+2)/3$ is recovered as previously derived in [21] for the SN equation. Subsequently, conserved quantities associated to the (generalized) LLN equation are also exhibited.

math-ph↗

arXiv2019

How does the photon's spin affect Gravitational Wave measurements?

We study the effect of the polarization of light beams on the time delay measured in Gravitational Wave experiments. To this end, we consider the Mathisson-Papapetrou-Dixon equations in a gravitational wave background, with two of the possible spin supplementary conditions: by Frenkel-Pirani, or by Tulczyjew. In the first case, photons follow a null geodesic and thus no spin effect is present. The second case shows a deviation of the photons from the null geodesic, resulting in a tiny effect on the measured time delay of photons depending on their polarization state.

gr-qc↗