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

Daniel Canarutto

Archivum Mathematicum (2018)

  • Volume: 054, Issue: 4, page 205-226
  • ISSN: 0044-8753

Abstract

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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 S M 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 X : M → M , turn out to be well-defined without making any special assumption about X , and fulfill natural mutual relations.

How to cite

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Canarutto, Daniel. "Two-spinor tetrad and Lie derivatives of Einstein-Cartan-Dirac fields." Archivum Mathematicum 054.4 (2018): 205-226. <http://eudml.org/doc/294755>.

@article{Canarutto2018,
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 $\{\scriptstyle X\}\colon M\rightarrow M$, turn out to be well-defined without making any special assumption about $\{\scriptstyle X\}$, and fulfill natural mutual relations.},
author = {Canarutto, Daniel},
journal = {Archivum Mathematicum},
keywords = {Lie derivatives of spinors; Lie derivatives of spinor connections; deformed tetrad gravity},
language = {eng},
number = {4},
pages = {205-226},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Two-spinor tetrad and Lie derivatives of Einstein-Cartan-Dirac fields},
url = {http://eudml.org/doc/294755},
volume = {054},
year = {2018},
}

TY - JOUR
AU - Canarutto, Daniel
TI - Two-spinor tetrad and Lie derivatives of Einstein-Cartan-Dirac fields
JO - Archivum Mathematicum
PY - 2018
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 054
IS - 4
SP - 205
EP - 226
AB - 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.
LA - eng
KW - Lie derivatives of spinors; Lie derivatives of spinor connections; deformed tetrad gravity
UR - http://eudml.org/doc/294755
ER -

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