q-Oscillators, q-Epsilon Tensor, q-Groups

Abstract

Considering a multi-dimensional $q$-oscillator invariant under the (non quantum) group $U(n)$, we construct a $q$-deformed Levi-Civita epsilon tensor from the inner product states. The invariance of this $q$-epsilon tensor is shown to yield the quantum group $S{L}_q(n)$ and establishes the relationship of the $U(n)$ invariant $q$-oscillator to quantum groups and quantum group related oscillators. Furthermore the $q$-epsilon tensor provides the connection between $S{L}_q(n)$ and the volume element of the quantum hyper plane.

11 pages

Cited by in corpus (1)

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