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

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

1993-08-19

arxiv.org/abs/hep-th/9308096v1

Phys.Lett. B321 (1994) 385

Physics

High Energy Physics

High Energy Physics - Theory

11 pages

Scientific paper

10.1016/0370-2693(94)90263-1

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 $SL_{q}(n)$ 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 $SL_{q}(n)$ and the volume element of the quantum hyper plane.

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