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Summary of my publications

My work is focused on geometry and symmetry in physics, in particular how they shape the equations of motion for elementary systems. While much of modern theoretical physics is built upon the Poincaré group, I focus on lesser known kinematical groups, notably the Carroll group, and their applications across gravitational physics, optics, condensed matter, and potentially others.

The dynamics of photons

A major topic in my research is about investigating how spin affects the motion of particles in curved spacetime. The Mathisson-Papapetrou-Dixon equations provide the general framework for describing spinning test particles (which includes elementary particles with their spin, such as the photon) in general relativity, but they are often neglected in favor of the easier to use, and often sufficient, geodesic equations.

In my first article [1], I studied the propagation of light (with spin) in Schwarzschild spacetime, showing that photons of different polarizations follow slightly different trajectoires, which is called gravitational birefringence. This effect arises from the coupling between the photon’s spin and spacetime curvature. This coupling, and hence the deviation to the geodesic, depends both on the helicity of the photon and its wavelength.

I then studied photons in a gravitational wave backgrounds in [2], calculating the spin-induced deviations for the time of flight for photons in gravitational wave detectors. This effect is however many order of magnitude outside the experimental bounds of detectors such as Virgo or LIGO.

Most recently, in [9], we have extended the Mathisson-Papapetrou-Dixon equations of motion to (pseudo-)Finsler geometry. While standard general relativity uses pseudo-Riemannian geometry, Finsler geometry allows for direction-dependent properties of spacetime. This geometry is relevant in optics (for example the speed of light in some birefringent crystal depends on the direction in the crystal), some effective field theories, and other contexts. Technically, this is done by following both the ideas of Mathisson, and of Souriau, where one calculates the distribution of energy momentum tensor of the world line of the particle (Mathisson) by requiring diffeomorphism invariance (Souriau), the latter making it a straightforward (although long and tedious) computation for Finsler spacetimes.

Carroll Symmetry

In parallel to the above considerations, I have also worked on Carroll symmetry (named after Lewis Carroll by Lévy-Leblond). As shown by Bacry and Lévy-Leblond, this symmetry group is one of the three main spacetime symmetry group, along the Poincaré and Galilean symmetry groups. Carroll symmetries/geometries emerge naturally on null hypersurfaces in general relativity, such as black hole horizons or null infinity, and also in condensed matter ("flat-bands" systems in particular). Generally, Carroll particles famously cannot move, but in 2+1 "planar" dimensions, which is the dimensions of all typical physical applications where Carroll is relevant, the structure of this group is richer, in that it admits two central extensions.

I have shown in [5] that planar Carroll particles, when considering these central extensions, can actually move, and exhibit non-trivial Hall-like motions when coupled to electromagnetic fields. The two central extension parameters act as intrinsic "exotic" and "magnetic" charges, which combine with external fields to produce effective forces.

In [6], we showed that these effects manifest on the horizons of Kerr-Newman black holes, where "exotic photons" (massless, chargeless particles with anyonic spin and magnetic moments), stuck on the horizon, drift azimuthally in response to the horizon's magnetic field.

In a review [7], we showed that Carroll symmetry also describes the physics of fractons, which are quasiparticles in condensed matter systems with restricted mobility due to conserved dipole moments. We showed that fracton dipole conservation is mathematically equivalent to Carroll boost symmetry.

I have also explored different realizations of Carrollian dynamics as effective theories on null hypersurfaces in Lorentzian spacetimes in [8]. This helps to provide physical interpretations for Carrollian quantities that are difficult to understand in purely intrinsic formulations, and shows that non trivial planar Carroll dynamics can be thought of as a gateway to ambient theories where light does not propagate on geodesics, echoing my work on spinning light.

Miscellaneous geometrical works

In [3], we defined the Lévy-Leblond--Newton equation to describe non-relativistic fermions, which are subject to their own gravtitational potential. We formulated it both in a "standard" form, and also in a geometrical way on a Bargmann geometry. This geometric writing is very natural, in that it simply corresponds to a massless Dirac equation on this space. This allowed us to easily compute the symmetry group of this equation and the corresponding dynamical exponent.

Lastly, in [4], we extended the dressing field method to 2-frame bundles. The dressing field method systematically reduces gauge symmetries of Cartan connections, yielding local, mostly gauge-invariant connections, and provides a "top-down" approach to define tractor bundles. Applying this method to 2-frame bundles, we showed that we can build the (known) conformal tractor bundle, but also the (new) projective tractor bundle, in a canonical and constructive way.

List of publications by writing order

[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]