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arXiv · 0705.1675

Spinor calculus for q-deformed quantum spaces II

Alexander Schmidt·Hartmut Wachter
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Abstract

This is the second part of an article about q-deformed analogs of spinor calculus. The considerations refer to quantum spaces of physical interest, i.e. q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. The Clifford algebras corresponding to these quantum spaces are treated. Especially, their commutation relations and their Hopf structures are written down. Bases of the four-dimensional Clifford algebras are constructed and their properties are discussed. Matrix representations of the Clifford algebras lead to q-deformed Dirac-matrices for the four-dimensional quantum spaces. Moreover, q-analogs of the four-dimensional spin matrices are presented. A very complete set of trace relations and rearrangement formulae concerning spin and Dirac-matrices is given. Dirac spinors together with their bilinear covariants are defined. Their behavior under q-deformed Lorentz transformation is discussed in detail.

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Alexander Schmidt, Hartmut Wachter. 2007-05-11. Spinor calculus for q-deformed quantum spaces II. https://arxiv.org/abs/0705.1675

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