A modular spectral triple for K-Minkowski space

JOURNAL OF GEOMETRY AND PHYSICS

卷:76

Article

Matassa, Marco

关键词: Non-commutative geometry;    Spectral triple;    Hopf algebra;    Spectral dimension;   

DOI  :  10.1016/j.geomphys.2013.10.023

来源: Elsevier

【 摘 要 】

We present a spectral triple for K-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the K-Poincare algebra. The weight satisfies a KMS condition and its associated modular operator plays an important role in the construction. This forces us to introduce two ingredients which have a modular flavour: the first is a twisted commutator, used to obtain a boundedness condition for the Dirac operator, and the second is a weight replacing the usual operator trace, used to measure the growth of the resolvent of the Dirac operator. We show that, under some assumptions related to the symmetries and the classical limit, there is a unique Dirac operator and automorphism such that the twisted commutator is bounded. Then, using the weight mentioned above, we compute the spectral dimension associated to the spectral triple and find that is equal to the classical dimension. Finally we briefly discuss the introduction of a real structure. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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