Local spin base invariance from a global differential-geometrical point of view, Claudio Emmrich (TPI Jena)

Thursday 12 May 2022, 14:15 → 15:45 Europe/Berlin

Abbeanum/Ground floor-HS 2 - Hörsaal 2 (TPI, FSU Jena)

Local spin base invariance is the extension of the global symmetry the 
gamma matrices under similarity transformations to a local symmetry, 
decoupling coordinate/Lorentz transformations, thus turning Dirac 
spinors to “scalars under Lorentz transformations” in an appropriate 
sense. In this talk, I will give a global geometric interpretation of 
the local spin base formulation on a curved space-time and in particular 
of its central element, the global Dirac structure, in terms of 
principal and vector bundles and their endomorphisms. It is shown that 
this is intimately related to spin and spin-C-structures in the sense 
that the existence of one of those implies the existence of a Dirac 
structure and allows an extension to local spin base invariance. Vice 
versa, the existence of a Dirac structure implies the existence of a 
Spin-C structure. Furthermore, arguments are given that the Dirac 
structure is a more natural choice as a variable for (quantum) gravity 
than tetrads/vielbeins.