1212.3462 (Marco Matassa)

A modular spectral triple for $κ$-Minkowski space    [PDF]

Marco Matassa

We present a spectral triple associated to $\kappa$-Minkowski space in two dimensions. Starting from an algebra naturally associated with $\kappa$-Minkowski space, a Hilbert space is built using a weight which is invariant under the $\kappa$-Poincar\'e algebra. This weight satisfies the KMS condition and is related to the modular properties of this geometry. This forces us to use two ingredients which have a modular flavor: the first is a twisted commutator to obtain the boundedness of commutators of the Dirac operator with an element of the algebra, the second is the use of a weight to measure the growth of the resolvent of the Dirac operator. We show that there is a natural choice for the Dirac operator and the automorphism defining the twisted commutator. We compute the spectral dimension associated to this spectral triple and find that is equal to the classical dimension. Finally we briefly discuss the introduction of a real structure.

View original: http://arxiv.org/abs/1212.3462