Unitary representations of N-conformal Galilei group

TL;DR

This paper constructs all unitary irreducible representations of the centrally extended N-conformal Galilei group for odd N and derives the group's on-shell action, connecting it to previous results in the literature.

Contribution

It provides a complete classification of unitary irreducible representations for the N-conformal Galilei group with odd N, extending prior work on the group's dynamics.

Findings

Constructed all unitary irreducible representations for the group.

Derived the on-shell action of the group.

Connected the derived action to previous results.

Abstract

All unitary irreducible representations of centrally extended (N-odd) N-conformal Galilei group are constructed. The "on-shell" action of the group is derived and shown to coincide, in special but most important case, with that obtained in: J. Gomis, K. Kamimura, Phys. Rev. {\bf D85} (2012), 045023.