The Braided Heisenberg Group

Details The Braided Heisenberg Group The Braided Heisenberg Group

1992-10-08

arxiv.org/abs/hep-th/9210042v1

J.Math.Phys. 34 (1993) 3588-3606

Physics

High Energy Physics

High Energy Physics - Theory

33 pages

Scientific paper

10.1063/1.530047

We compute the braided groups and braided matrices $B(R)$ for the solution $R$ of the Yang-Baxter equation associated to the quantum Heisenberg group. We also show that a particular extension of the quantum Heisenberg group is dual to the Heisenberg universal enveloping algebra $U_{q}(h)$, and use this result to derive an action of $U_{q}(h)$ on the braided groups. We then demonstrate the various covariance properties using the braided Heisenberg group as an explicit example. In addition, the braided Heisenberg group is found to be self-dual. Finally, we discuss a physical application to a system of n braided harmonic oscillators. An isomorphism is found between the n-fold braided and unbraided tensor products, and the usual `free' time evolution is shown to be equivalent to an action of a primitive generator of $U_{q}(h)$ on the braided tensor product.

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