Approach to Quantum Group deformed Quantum Field Theory

Abstract

In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U(\infty )$ group. Here it is shown how to define an appropriate $U_q(\infty )$ which then leads to deformed commutation relations. A formalism that was previously defined for quantum group symmetric quantum mechanics can be applied by imposing simple adjustments. The simplest example of a free scalar $q$-bosonic field is discussed. The deformation occurs as a multi-particle effect, which introduces a kinetic energy (i.e. $(\vec{p}{)}^2$) - ordering of the involved particles.

6 pages; Withdrawn at author's request Mon, 30 Oct 95