Self-dual and anti-self-dual structure of the de Sitter gauge theory and Ashtekar's variables

Details Self-dual and anti-self-dual structure of the de Sitter gauge theory and Ashtekar's variables Self-dual and anti-self-dual structure of the de Sitter gauge theory and Ashtekar's variables

Nov 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996phrvd..54.6552c&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 54, Issue 10, 15 November 1996, pp.6552-6554

Mathematics

Logic

7

Fundamental Problems And General Formalism, Canonical Formalism, Lagrangians, And Variational Principles, Gravity In More Than Four Dimensions, Kaluza-Klein Theory, Unified Field Theories, Alternative Theories Of Gravity, Canonical Quantization

Scientific paper

A Yang-Mills-like theory of gravity, which is a de Sitter gauge theory, is presented starting from a Clifford algebra C(3,1) generated by the Dirac matrices. The self-dual and anti-self-dual structure of the quadratic terms in the curvature with respect to internal as well as external indices is investigated and then a Yang-Mills-like Lagrangian for the de Sitter gauge theory is obtained which involves no torsion term and returns to Ashtekar's Lagrangian naturally modulo topological and cosmological terms.

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