Quantisation of a particle moving on a group manifold

Abstract

The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G\times G$, there is a very natural way to ``factorise" the theory so that only one copy of the global symmetry is preserved. In the case of $G=SU(2)$, a simple deformation of the quantised theory is proposed to give a realisation of the quantum group, $U_t(SL(2))$. The symplectic structures of the corresponding classical theory is derived. This can be used, in principle, to obtain a Lagrangian formulation for the $U_t(SL(2))$ symmetry.

DAMTP-94-41, 11 pages

References in corpus (1)

• Symplectic structures associated to Lie-Poisson groups

Cited by in corpus (13)

• The Schwarzian Theory - A Wilson Line Perspective
• Fine Structure of Jackiw-Teitelboim Quantum Gravity
• Deformation Quantization of Superintegrable Systems and Nambu Mechanics
• Chiral Extensions of the WZNW Phase Space, Poisson-Lie Symmetries and Groupoids
• Quantisation of the SU(N) WZW Model at Level $k$
• On 2D gauge theories in Jackiw-Teitelboim gravity
• Chiral Quantization of the WZW $SU(n)$ Model
• Note on global symmetry and SYK model
• Canonical quantization of a massive particle on $Ad{S}_3$
• A Diffusion Model for SU(N) QCD Screening
• Classical Wakimoto Realizations of Chiral WZNW Bloch Waves
• Open strings in Lie groups and associative products
• Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes