36 research outputs found
Gauge Theory and a Dirac Operator on a Noncommutative Space
As a tool to carry out the quantization of gauge theory on a noncommutative
space, we present a Dirac operator that behaves as a line element of the
canonical noncommutative space. Utilizing this operator, we construct the
Dixmier trace, which is the regularized trace for infinite-dimensional
matrices. We propose the possibility of solving the cosmological constant
problem by applying our gauge theory on the noncommutative space.Comment: 2 figures, final versio
Supersymmetric Field Theories on Noncommutative Spaces
Supersymmetric field theories on noncommutative spaces are constructed. We
present two different representations of noncommutative space, but we can
obtain supersymmetry algebla and supersymmetric Yang-Mills action independent
of its representation. As a result, we will see that the action has a close
relationship with IIB matrix model
Unitary-Matrix Integration on 2D Yang-Mills Action
Using the idea of Itzykson-Zuber integral, unitary-matrix integration of 2D
Yang-Mills action is presented. The uniqueness of the solution of heat equation
enables us to integrate out the unitary-matrix parts of hermite matrices and to
obtain the expression of integration over vectors, also in this case.Comment: 8 page
Cyclic Universe \`{a} la string theory
We shall present a model of the "cyclic universe" that can be constructed
only by assuming a minimal set of properties of string theory. We clarify our
viewpoint of the cyclic universe and show some attempts to mateliarize the idea
as field theoretical manner.Comment: Proceeding of International Workshop "Frontier of Quantum Physics"
February 17(Thu.)-19(Sat.) 200
Dirac Sea and Hole Theory for Bosons II -- Renormalization Approach --
In bosonic formulation of the negative energy sea, so called Dirac sea
presented in the preceding paper [arXiv:hep-th/0603242], one of the crucial
points is how to construct a positive definite inner product in the negative
energy states, since naive attempts would lead to non-positive definite ones.
In the preceding paper the non-local method is used to define the positive
definite inner product. In the present article we make use of a kind of
-regularization and renormalization method which may clarify
transparently the analytical properties of our formulation.Comment: 10 pages, 2 figures; Section 4 is inserte