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arXiv · hep-th/9407116

Quantisation of a particle moving on a group manifold

Meifang Chu·Peter Goddard
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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.

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Meifang Chu, Peter Goddard. 1994-07-19. Quantisation of a particle moving on a group manifold. https://doi.org/10.1016/0370-2693(94)90977-6

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