Galilei particles revisited
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.
Authors
- José Miguel Figueroa-O'Farrill (ORCID: https://orcid.org/0000-0002-9308-9360)
- Alfredo Pérez (ORCID: https://orcid.org/0000-0003-0989-9959)
- Simon Pekar (ORCID: https://orcid.org/0000-0002-0765-8986)
- Stefan Prohazka (ORCID: https://orcid.org/0000-0002-3925-3983)
Institutions
- Centre National de la Recherche Scientifique (FR)
- University of Vienna (AT)
- École Polytechnique (FR)
- San Sebastián University (CL)
- Centre de Physique Théorique (FR)
- Maxwell Institute for Mathematical Sciences (GB)
- Institut Polytechnique de Paris (FR)
- Centro de Estudios Científicos (CL)
Publication Details
- Journal
- SciPost Physics Lecture Notes
- Published
- 2025-03-13
- DOI
- https://doi.org/10.21468/scipostphyslectnotes.93
- Citations
- 2
- Primary Topic
- Quantum Mechanics and Applications
- Type
- article
- Field-Weighted Citation Impact
- 2.49
Funders
- Fonds De La Recherche Scientifique - FNRS
- École Polytechnique, Université Paris-Saclay
- Fondo Nacional de Desarrollo Científico y Tecnológico