This is an introduction for nonspecialists to the noncommutative geometric approach to
Planck scale physics coming out of quantum groups. The canonical role of the 'Planck scale …

We develop a general framework for quantum field theory on noncommutative spaces, ie,
spaces with quantum group symmetry. We use the path integral approach to obtain …

An algebraic theory of integration on quantum planes and other braided spaces is
introduced. In the one‐dimensional case a novel picture of the Jackson q‐integral as …

We study the q-deformed fuzzy sphere, which is related to D-branes on SU (2) WZW models,
for both real q and qa root of unity. We construct for both cases a differential calculus which …

We study the second quantization of field theory on the q-deformed fuzzy sphere for q∈ R.
This is performed using a path integral over the modes, which generate a quasi-associative …

It is often thought that quantum groups provide the key to q-deforming the basic structures of
physics from the point of view of noncommutative geometry. If one considered a classical …

We construct differential calculi on multiparametric quantum orthogonal planes in any
dimension N. These calculi are bicovariant under the action of the full inhomogeneous …

A generalized harmonic oscillator on noncommutative spaces is considered. Dynamical
symmetries and physical equivalence of noncommutative systems with the same energy …

By the application of the general twist-induced⋆-deformation procedure we translate second
quantization of a system of bosons/fermions on a symmetric spacetime into a …

We propose a solution to the problem of compatibility of Bose-Fermi statistics with symmetry
transformations implemented by compact quantum groups of Drinfel'd type. We use unitary …