A ] 3 S ep 2 00 7 QUANTUM GROUPS ACTING ON 4 POINTS

5 M ar 2 00 7 QUANTUM GROUPS ACTING ON 4 POINTS

We classify the compact quantum groups acting on 4 points. These are the quantum subgroups of the quantum permutation group Q4. Our main tool is a new presentation for the algebra C(Q4), corresponding to an isomorphism of type Q4 ≃ SO−1(3). The quantum subgroups of Q4 are subject to a McKay type correspondence, that we describe at the level of algebraic invariants.

X iv : h ep - t h / 04 09 10 3 v 1 8 S ep 2 00 4 Duality Mechanism by Introduction of Gauge Condensates

In this work we will present a method to employ a duality mechanism via introduction of gauge condensates on fully quantized topological Schwarz type actions. The restrictions in implementing this equivalence at quantum level is discussed and, some three-dimensional examples are presented.

ar X iv : m at h - ph / 0 10 80 18 v 2 7 S ep 2 00 1 Symmetries of complexified space - time and algebraic structures ( in quantum theory )

Symmetries of complexified space-time and algebraic structures (in quantum theory). Abstract In the paper is discussed description of some algebraic structures in quantum theory by using formal recursive constructions with " complex Poincaré group " ISO(4, C).

ar X iv : h ep - t h / 04 08 12 5 v 1 1 7 A ug 2 00 4 Field theoretic models on covariant quantum spaces

ar X iv : h ep - t h / 03 09 07 8 v 2 7 O ct 2 00 3 Equivalence of Many - Photon Green Functions in DKP and KGF Statistical Quantum Field Theories

We prove the equivalence of many-photon Green functions in statistical quantum field Duffin-Kemmer-Petiau (DKP) and Klein-GordonFock (KGF) theories using functional path integral formalism for partition functional in statistical quantum (finite temperature) field theory. We also calculate the polarization operators in these theories in oneloop approximation, and demonstrate their coincidence.