Stochastic Covariant Derivatives in a (Curved) SpaceTime: a Glimpse into the Fractoid Spaces
Abstract
A study on the notion of covariant derivatives in flat and curved spacetime via ItôWiener processes, when subjected to stochastic processes, is presented. Going into details, there is an analysis of the following topics: (i) Besov space, (ii) Schrödinger operators, (iii) KleinGordon and Dirac equations, (iv) Dirac operator via Clifford connection, (v) semimartingale and Stratonovich integral, (vi) stochastic geodesics, (vii) white noise on a (4+)D spacetime $\mathfrak{H}$geometry (with the PaleyWiener integral), and (viii) torsion of the covariant derivative. In the background stands the scale relativity theory, together with a sketch of the concept of fractoid spaces.
 Publication:

arXiv eprints
 Pub Date:
 March 2023
 DOI:
 10.48550/arXiv.2303.10177
 arXiv:
 arXiv:2303.10177
 Bibcode:
 2023arXiv230310177N
 Keywords:

 Mathematics  Probability;
 Mathematics  Differential Geometry
 EPrint:
 Minor corrections and additions