Galilei particles revisited
arXiv:2401.03241 · doi:10.21468/SciPostPhysLectNotes.93
Abstract
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.
arXiv comment32 pages, 1 figure
References in corpus (16)
- Fractons
- Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
- Fracton Phases of Matter
- Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
- Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
- Towards classification of Fracton phases: the multipole algebra
- Fractons, dipole symmetries and curved spacetime
- BMS Particles in Three Dimensions
- Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
- Geometrical Spinoptics and the Optical Hall Effect
- Spatially isotropic homogeneous spacetimes
- Carroll/fracton particles and their correspondence
- Geometric action for extended Bondi-Metzner-Sachs group in four dimensions
- Non-Lorentzian theories with and without constraints
- Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part I: Generalities and Vectorial Descriptions
- Snowmass White Paper: Effective Field Theories for Condensed Matter Systems