This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a classification scheme for different generalizations is obtained. The framework is based on wavelets (coherent states) in Banach spaces generated by “admissib...

In this lecture I will report on some recent progress in understanding the relation of Dirac operators on Clifford modules over an even-dimensional closed Riemannian manifold M and (euclidean) Einstein-Yang-Mills-Higgs models. Lecture at the IV th Conference on Clifford Algebras and their Applications in Mathematical Physics, Aachen, Germany, May 28 31, 1996 Although being a gauge theory, it is...

We propose a new framework for constructing geometric and physical models on nonholonomic manifolds provided both with Clifford – Lie algebroid symmetry and nonlinear connection structure. Explicit parametrizations of generic off–diagonal metrics and linear and nonlinear connections define different types of Finsler, Lagrange and/or Riemann–Cartan spaces. A generalization to spinor fields and D...

Finite quantum field theories may be constructed from the most general renormalizable quantum field theory by forbidding, order by order in the perturbative loop expansion, all ultraviolet-divergent renormalizations of the physical parameters of the theory. The relevant finiteness conditions resulting from this requirement relate all dimensionless couplings in the theory. At first sight, Yukawa...

This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a classification scheme for different generalizations is obtained. The framework is based on wavelets (coherent states) in Banach spaces generated by “admissib...

Bazzoni’s Conjecture states that the Prüfer domain R has finite character if and only if R has the property that an ideal of R is finitely generated if and only if it is locally principal. In [4] the authors use the language and results from the theory of lattice-ordered groups to show that the conjecture is true. In this article we supply a purely ring theoretic proof. 1. Bazzoni’s Conjecture ...

We use Dirac matrix representations of the Clifford algebra to build fracton models on lattice and their effective Chern-Simons-like theory. As an example we fractons in odd $D$ spatial dimensions $(D+1)$ The model possesses anti-symmetric $K$ resembling that hierarchical quantum Hall states. gauge charges are conserved sub-dimensional manifolds which ensures fractonic behavior. construction ex...