36 research outputs found

    Gauge Theory and a Dirac Operator on a Noncommutative Space

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    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

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    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

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    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

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    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 --

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    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 ϵ\epsilon-regularization and renormalization method which may clarify transparently the analytical properties of our formulation.Comment: 10 pages, 2 figures; Section 4 is inserte
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