This paper discusses the formulation of the non-commutative Chern-Simons (CS) theory where the spatial slice, an infinite strip, is a manifold with boundaries. As standard ∗products are not correct for such manifolds, the standard non-commutative CS theory is not also appropriate here. Instead we formulate a new finite-dimensional matrix CS model as an approximation to the CS theory on the stri...

X iv :q ua nt -p h/ 03 05 15 0v 1 2 4 M ay 2 00 3 Particle and Field Symmetries and Noncommutative Geometry Ajay Patwardhan Physics Department, St.Xavier’s College, Mahapalika Marg, Mumbai 400001, India. * e-mail : [email protected] Abstract The development of Noncommutative geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and d...

1.1. We denote by V a connected ^-dimensional complete Riemannian manifold, by d = d(V) the diameter of V, and by c = c(V) and c~ = c~(V), respectively, the upper and lower bounds of the sectional curvature of V. We set c = c(V) = max (| c1, | c~ |). We say that F i s ε-flat, ε > 0, if cd < ε. 1.2. Examples. a. Every compact flat manifold is ε-flat for any ε > 0. b. Every compact nil-manifold p...

In this paper we describe an approach to differential topology and geometry rooted in supersymmetric quantum theory. We show how the basic concepts and notions of differential geometry emerge from concepts and notions of the quantum theory of non-relativistic particles with spin, and how the classification of different types of differential geometry follows the classification of supersymmetries...

A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in very much the same way we are used to from the geometrical arena underlying classical physical theories and models. In previous work, certain differential cal...

 In this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper K-ideals. These definitions are thegeneralizations of the definitions of commutative, andimplicative hyper K-ideals, respectively, which have been definedin [12]. Then we obtain some related results. In particular wedetermine the relationships between n-fold implicative hyperK-ideal and n-fol...

In this paper one considers three homotopy functors on the category of manifolds , hH∗, cH∗, sH∗, and parallel them with other three homotopy functors on the category of connected commutative differential graded algebras, HH∗, CH∗, SH∗. If P is a smooth 1-connected manifold and the algebra is the de-Rham algebra of P the two pairs of functors agree but in general do not. The functors HH∗ and CH...

The homotopical information hidden in a supersymmetric structure is revealed by considering deformations of a configuration manifold. This is in sharp contrast to the usual standpoints such as Connes’ programme where a geometrical structure is rigidly fixed. For instance, we can relate supersymmetries of types N = 2n and N = (n, n) in spite of their gap due to distinction between Z2(even-odd)an...