Operator Theory on Noncommutative Varieties Ii
ثبت نشده
چکیده
منابع مشابه
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....
متن کاملGauge 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...
متن کاملOperator space embedding of Lq into Lp
The idea of replacing functions by linear operators, the process of quantization, goes back to the foundations of quantum mechanics and has a great impact in mathematics. This applies for instance to representation theory, operator algebra, noncommutative geometry, quantum and free probability or operator space theory. The quantization of measure theory leads to the theory of Lp spaces defined ...
متن کاملTitle: Solvmanifolds and Noncommutative Tori with Real Multiplication
We prove that the Shimizu L-function of a real quadratic field is obtained from a (Lorentzian) spectral triple on a noncommutative torus with real multiplication, as an adiabatic limit of the Dirac operator on a 3-dimensional solvmanifold. The Dirac operator on this 3dimensional geometry gives, via the Connes-Landi isospectral deformations, a spectral triple for the noncommutative tori obtained...
متن کاملSolvmanifolds and noncommutative tori with real multiplication
We prove that the Shimizu L-function of a real quadratic field is obtained from a (Lorentzian) spectral triple on a noncommutative torus with real multiplication, as an adiabatic limit of the Dirac operator on a 3-dimensional solvmanifold. The Dirac operator on this 3-dimensional geometry gives, via the Connes–Landi isospectral deformations, a spectral triple for the noncommutative tori obtaine...
متن کامل