Quantisation of a particle moving on a group manifold

Details Quantisation of a particle moving on a group manifold Quantisation of a particle moving on a group manifold

1994-07-19

arxiv.org/abs/hep-th/9407116v1

Phys.Lett. B337 (1994) 285-293

Physics

High Energy Physics

High Energy Physics - Theory

DAMTP-94-41, 11 pages

Scientific paper

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.

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