Alladi Ramakrishnan Hall

Spectral Distance in Non-commutative Lorentzian Plane

Anwesha Chakraborty

S. N. Bose National Centre for Basic Sciences, Kolkata

In his formulation of Non-commutative geometry (NCG) and its subsequent application to standard model of particle physics , Alain Connes has essentially dealt with spaces with Euclidean signature i.e. Riemannian manifold. This feature of his formulation has remained a sort of a bottle-neck in the further development in its application and eventual reconciliation with the realistic nature of our space-time, which as we all know to be as a manifold with Lorentzian signature. Attempts are being made for quite some time now and people have devised various ways to circumvent this problem like the so called “Wick rotation” etc. Recent activities in this direction indicates that there is still no consensus in the literature about its axiomatic formulation . Despite the fact, we would like to follow the work of [N. Franco et. al.], in our preliminary attempt to compute the spectral distance between a pair of time-like separated events associated with pure states in Lorentzian Moyal plane where we use Hilbert-Schmidt operator formulation of NC quantum mechanics and show that this axiomatic formulations serves our purpose quite adequately. The result shows no deformations of non-commutative origin, as in the Euclidean case.

Ref: Arxiv: 1910.00010