TY - JOUR
T1 - Galilei particles revisited
AU - Figueroa-O'Farrill, José Miguel
AU - Pekar, Simon
AU - Pérez, Alfredo
AU - Prohazka, Stefan
N1 - Publisher Copyright:
Copyright J. M. Figueroa-O'Farrill et al.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/105001342544
U2 - 10.21468/SciPostPhysLectNotes.93
DO - 10.21468/SciPostPhysLectNotes.93
M3 - Article
AN - SCOPUS:105001342544
SN - 2590-1990
SP - 1
EP - 42
JO - SciPost Physics Lecture Notes
JF - SciPost Physics Lecture Notes
IS - 93
ER -