Differential Calculi on Quantum (Sub-) Groups and Their Classical Limit

Details Differential Calculi on Quantum (Sub-) Groups and Their Classical Limit Differential Calculi on Quantum (Sub-) Groups and Their Classical Limit

1994-01-28

arxiv.org/abs/hep-th/9401152v1

Physics

High Energy Physics

High Energy Physics - Theory

contribution to the proceedings of the International Symposium ``Generalized Symmetries in Physics'' (ASI Clausthal 1993), 12

Scientific paper

For the two-parameter matrix quantum group GLp,q(2) all bicovariant differential calculi (with a four-dimensional space of 1-forms) are known. They form a one-parameter family. Here, we give an improved presentation of previous results by using a different parametrization. We also discuss different ways to obtain bicovariant calculi on the quantum subgroup SLq(2). For those calculi, we do not obtain the ordinary differential calculus on SL(2) in the classical limit. The structure which emerges here can be generalized to a nonstandard differential calculus on an arbitrary differentiable manifold and exhibits relations with stochastic calculus and `proper time' relativistic quantum theories.

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