Path integrals on sl(2, R) orbits - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2022

Path integrals on sl(2, R) orbits

Résumé

We quantise orbits of the adjoint group action on elements of the sl Lie algebra. The path integration along elliptic slices is akin to the coadjoint orbit quantization of compact Lie groups, and the calculation of the characters of elliptic group elements proceeds along the same lines as in compact groups. The computation of the trace of hyperbolic group elements in a diagonal basis as well as the calculation of the full group action on a hyperbolic basis requires considerably more technique. We determine the action of hyperbolic one-parameter subgroups of PSL on the adjoint orbits and discuss global subtleties in choices of adapted coordinate systems. Using the hyperbolic slicing of orbits, we describe the quantum mechanics of an irreducible sl representation in a hyperbolic basis and relate the basis to the mathematics of the Mellin integral transform. We moreover discuss the representation theory of the double cover SL of PSL as well as that of its universal cover. Traces in the representations of these groups for both elliptic and hyperbolic elements are computed. Finally, we motivate our treatment of this elementary quantization problem by indicating applications.

Dates et versions

hal-03645262 , version 1 (19-04-2022)

Identifiants

Citer

Sujay K. Ashok, Jan Troost. Path integrals on sl(2, R) orbits. Journal of Physics A: Mathematical and Theoretical, 2022, 55 (33), pp.335202. ⟨10.1088/1751-8121/ac802c⟩. ⟨hal-03645262⟩
18 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More