Grassmann variables on quantum spaces

Details Grassmann variables on quantum spaces Grassmann variables on quantum spaces

2004-07-30

arxiv.org/abs/hep-th/0407273v3

Eur. Phys. J. C 45 (2006) 529

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, Latex, crossing symmetries for representations have been simplified, section with general information has been added

Scientific paper

10.1140/epjc/s2005-02441-4

Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each case standard techniques for dealing with q-deformed Grassmann variables are developed. Formulae for multiplying supernumbers are given. The actions of symmetry generators and fermionic derivatives upon antisymmetrized quantum spaces are calculated. The complete Hopf structure for all types of quantum space generators is written down. From the formulae for the coproduct a realization of the L-matrices in terms of symmetry generators can be read off. The L-matrices together with the action of symmetry generators determine how quantum spaces of different type have to be fused together.

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