Address: Dipartimento di Matematica e Informatica “U. Dini”, Via S. Marta 3, 50139 Firenze, Italia
E-mail:
daniel.canarutto@unifi.it
http://www.dma.unifi.it/~canarutto
Abstract: An integrated approach to Lie derivatives of spinors, spinor connections and the gravitational field is presented, in the context of a previously proposed, partly original formulation of a theory of Einstein-Cartan-Maxwell-Dirac fields based on “minimal geometric data”: the needed underlying structure is determined, via geometric constructions, from the unique assumption of a complex vector bundle $SM$ with 2-dimensional fibers, called a $2$-spinor bundle. Any further considered object is assumed to be a dynamical field; these include the gravitational field, which is jointly represented by a soldering form (the tetrad) relating the tangent space $M$ to the $2$-spinor bundle, and a connection of the latter (spinor connection). The Lie derivatives of objects of all considered types, with respect to a vector field $\colon M\rightarrow M$, turn out to be well-defined without making any special assumption about $$, and fulfill natural mutual relations.
AMSclassification: primary 53B05; secondary 58A32, 83C60.
Keywords: Lie derivatives of spinors, Lie derivatives of spinor connections, deformed tetrad gravity.
DOI: 10.5817/AM2018-4-205