Contributor info: Dr Simon Pekar

José Miguel Figueroa-O'Farrill, Simon Pekar, Alfredo Pérez, Stefan Prohazka

SciPost Phys. Lect. Notes 93 (2025) · published 13 March 2025 | Toggle abstract · pdf

We revisit the classifications of classical and quantum galilean particles: that is, we fully classify homogeneous symplectic manifolds and unitary irreducible projective representations of the Galilei group. Equivalently, these are coadjoint orbits and unitary irreducible representations of the Bargmann group, the universal central extension of the Galilei group. We provide an action principle in each case, discuss the nonrelativistic limit, as well as exhibit, whenever possible, the unitary irreducible representations in terms of fields on Galilei spacetime. Motivated by a forthcoming study of planons we pay close attention to the mobility of the less familiar massless Galilei particles.

Jelle Hartong, Giandomenico Palumbo, Simon Pekar, Alfredo Perez, Stefan Prohazka

SciPost Phys. 18, 022 (2025) · published 17 January 2025 | Toggle abstract · pdf

We study dipole Chern–Simons theory with and without a cosmological constant in $2+1$ dimensions. We write the theory in a second order formulation and show that this leads to a fracton gauge theory coupled to Aristotelian geometry which can also be coupled to matter. This coupling exhibits the remarkable property of generalizing dipole gauge invariance to curved spacetimes, without placing any limitations on the possible geometries. We also use the second order formulation to construct a higher dimensional generalization of the action. Finally, for the $(2+1)$-dimensional Chern–Simons theory we find solutions and interpret these as electric monopoles, analyze their charges and argue that the asymptotic symmetries are infinite-dimensional.