SUq(n) Gauge Theory

SUq(2) lattice gauge theory.

Deformed Wong particles.

By generalizing the Feynman proof of the Lorentz force law, recently reported by Dyson, we derive equations of motion for particles possessing internal degrees of freedom I which do not, in general, generate a finite algebra. We obtain consistency criteria for the fields which interact with such particles. It is argued that when a particle with internal SUq(2) degrees of freedom is coupled to S...

Quantum group gauge theory on quantum spaces

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on SUq(2) . The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector...

Spectral equivalences and symmetry breaking in integrable SUq(N) spin chains with boundaries

We consider the SUq(N) invariant spin chain with diagonal and non-diagonal integrable boundary terms. The algebraic study of spin chains with different types of boundary terms is used to motivate a set of spectral equivalences between integrable chains with purely diagonal boundary terms and ones with an arbitrary non-diagonal term at one end. For each choice of diagonal boundary terms there is...

Advances in Quantum and Braided Geometry

We demonstrate our recent general results on the Casimir construction and moduli space of all bicovariant calculi by means of some detailed examples, including finitedifference and 2-jet cacluli on R and full details of the Casimir construction of the 4D calculus of SUq(2). We likewise demonstrate our previous general constructions with T. Brzezinski of quantum group gauge theory with examples ...