11,754 research outputs found
Covering and gluing of algebras and differential algebras
Extending work of Budzynski and Kondracki, we investigate coverings and
gluings of algebras and differential algebras. We describe in detail the gluing
of two quantum discs along their classical subspace, giving a C*-algebra
isomorphic to a certain Podles sphere, as well as the gluing of
U_{\sqrt{q}}(sl_2)-covariant differential calculi on the discs.Comment: latex2e, 27 page
Noncommutative generalization of SU(n)-principal fiber bundles: a review
This is an extended version of a communication made at the international
conference ``Noncommutative Geometry and Physics'' held at Orsay in april 2007.
In this proceeding, we make a review of some noncommutative constructions
connected to the ordinary fiber bundle theory. The noncommutative algebra is
the endomorphism algebra of a SU(n)-vector bundle, and its differential
calculus is based on its Lie algebra of derivations. It is shown that this
noncommutative geometry contains some of the most important constructions
introduced and used in the theory of connections on vector bundles, in
particular, what is needed to introduce gauge models in physics, and it also
contains naturally the essential aspects of the Higgs fields and its associated
mechanics of mass generation. It permits one also to extend some previous
constructions, as for instance symmetric reduction of (here noncommutative)
connections. From a mathematical point of view, these geometrico-algebraic
considerations highlight some new point on view, in particular we introduce a
new construction of the Chern characteristic classes
Van der Waerden calculus with commuting spinor variables and the Hilbert-Krein structure of the superspace
Working with anticommuting Weyl(or Mayorana) spinors in the framework of the
van der Waerden calculus is standard in supersymmetry. The natural frame for
rigorous supersymmetric quantum field theory makes use of operator-valued
superdistributions defined on supersymmetric test functions. In turn this makes
necessary a van der Waerden calculus in which the Grassmann variables
anticommute but the fermionic components are commutative instead of being
anticommutative. We work out such a calculus in view of applications to the
rigorous conceptual problems of the N=1 supersymmetric quantum field theory.Comment: 14 page
- …