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Galilei particles revisited
by José Miguel Figueroa-O'Farrill, Simon Pekar, Alfredo Pérez, Stefan Prohazka
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Submission summary
| Authors (as registered SciPost users): | José Figueroa-O'Farrill · Simon Pekar · Stefan Prohazka |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2401.03241v1 (pdf) |
| Date accepted: | Feb. 18, 2025 |
| Date submitted: | Jan. 17, 2024, 3:12 p.m. |
| Submitted by: | Figueroa-O'Farrill, José |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Published as SciPost Phys. Lect. Notes 93 (2025)
Reports on this Submission
Report
This is a good set of lecture notes on Galilean invariant systems. I found it to contain the essential features for a review and recommend it be accepted for publication.
Recommendation
Publish (meets expectations and criteria for this Journal)
Author: José Figueroa-O'Farrill on 2025-02-12 [id 5217]
(in reply to Report 1 on 2025-02-11)We are grateful to the referee for reading the paper and for their recommendation.