Uniqueness of $U_q(N)$ as a quantum gauge group and representations of its differential algebra

Details Uniqueness of $U_q(N)$ as a quantum gauge group and representations of its differential algebra Uniqueness of $U_q(N)$ as a quantum gauge group and representations of its differential algebra

1993-05-28

arxiv.org/abs/hep-th/9305176v2

Proc.Steklov Inst.Math.203:181-189,1994

Physics

High Energy Physics

High Energy Physics - Theory

14 pages (Changes in Introduction+changes in References+change in title)

Scientific paper

To construct a quantum group gauge theory one needs an algebra which is invariant under gauge transformations. The existence of this invariant algebra is closely related with the existence of a differential algebra $\delta _{{\cal H}} G_{q}$ compatible with the Hopf algebra structure. It is shown that $\delta _{{\cal H}} G_{q}$ exists only for the quantum group $U_{q}(N)$ and that the quantum group $SU_q(N)$ as a quantum gauge group is not allowed. The representations of the algebra $\delta _{{\cal H}} G_{q}$ are con- structed. The operators corresponding to the differentials are realized via derivations on the space of all irreducible *-representations of $U_q(2)$. With the help of this construction infinitesimal gauge transformations in two-dimensional classical space-time are described.

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