Fubini theorem in noncommutative geometry

Index Theorem in Finite Noncommutative Geometry

Noncommutative (NC) geometry is interesting since it is related to string theories and matrix models,1)–3) and it may capture some nature of quantum gravity. It is also a candidate for a new regularization of quantum field theory.4) Study about topological aspects of gauge theory on it is important since compactification of extra dimensions with nontrivial index in string theory can realize chi...

Symmetric Stable Processes and Fubini ' s Theorem

In the first half of this paper, a Fubini type identity in law which was previously developed by two of the authors between quadratic functionals of Brownian motion is extended in two directions: an analogue of this identity in law holds when Brownian motion is replaced by a symmetric stable process of any order a E (0,2), provided the function: x -* x2 is replaced by: x -> I x la; such Fubini ...

A stochastic Fubini theorem: BSDE method

In this paper, we prove a stochastic Fubini theorem by solving a special backward stochastic differential equation (BSDE, for short) which is different from the existing techniques. As an application, we obtain the well-posedness of a class of BSDEs with the Itô integral in drift term under a subtle Lipschitz condition.

Noncommutative geometry

Duality in Noncommutative Geometry

The structure of spacetime duality and discrete worldsheet symmetries of compactified string theory is examined within the framework of noncommutative geometry. The full noncommutative string spacetime is constructed using the Fröhlich-Gawȩdzki spectral triple which incorporates the vertex operator algebra of the string theory. The duality group appears naturally as a subgroup of the automorphi...