Two-spinor tetrad and Lie derivatives of Einstein-Cartan-Dirac fields

Canarutto, Daniel

Archivum mathematicum, Tome 54 (2018) no. 4, pp. 205-226

Abstract (VO)

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 ${\scriptstyle X}\colon M\rightarrow M$, turn out to be well-defined without making any special assumption about ${\scriptstyle X}$, and fulfill natural mutual relations.

Détail

DOI : 10.5817/AM2018-4-205

Classification : 53B05, 58A32, 83C60
Keywords: Lie derivatives of spinors; Lie derivatives of spinor connections; deformed tetrad gravity

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