Operator theory on noncommutative varieties, II

Operator Theory on Noncommutative Varieties Ii

Operator Theory on Noncommutative Varieties

We develop a dilation theory for row contractions T := [T1, . . . , Tn] subject to constraints such as p(T1, . . . , Tn) = 0, p ∈ P , where P is a set of noncommutative polynomials. The model n-tuple is the universal row contraction [B1, . . . , Bn] satisfying the same constraints as T , which turns out to be, in a certain sense, the maximal constrained piece of the n-tuple [S1, . . . , Sn] of ...

Operator Regularization and Noncommutative Chern Simons Theory

1 Abstract We examine noncommutative Chern Simons theory using operator regularization. Both the ζ-function and the η-function are needed to determine one loop effects. The contributions to these functions coming from the two point function is evaluated. The U(N) noncommu-tative model smoothly reduces to the SU(N) commutative model as the noncommutative parameter θ µν vanishes. 1 2 Introduction...

Gauge Theory and Dirac Operator on Noncommutative Space II Minkowskian and Euclidean Cases

In the preceding paper [arXiv:hep-th/0604217], we construct the Dirac operator and the integral on the canonical noncommutative space. As a matter of fact, they are ones on the noncommutative torus. In the present article, we introduce the method to extend to the Minkowskian and Euclidean cases. As a concluding remark, we present a geometrical notion of our gauge theory. 1 typeset using PTPTEX....

On Bilateral Weighted Shifts in Noncommutative Multivariable Operator Theory

We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these shifts, which has an appealing diagramatic interpretation in terms of an infinite tree structure associated with the underlying Hilbert space. These shifts arise naturally through weighted versions of certain representations of the Cuntz C...