New variables for gravity: Inclusion of matter

Details New variables for gravity: Inclusion of matter New variables for gravity: Inclusion of matter

Oct 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrvd..40.2572a&link_type=abstract

Physical Review D (Particles and Fields), Volume 40, Issue 8, 15 October 1989, pp.2572-2587

Mathematics

Logic

125

Scientific paper

The Lagrangian and Hamiltonian formulations of general relativity in terms of soldering forms and self-dual connections are extended to include matter sources and the cosmological constant. For matter sources we consider minimally coupled Klein-Gordon fields, complex- and Grassmann-valued Dirac fields, and Yang-Mills fields. Somewhat surprisingly, in spite of the derivative coupling in the spin-half fields, the use of only the self-dual part of the connection as a basic variable does not lead to spurious equations or inconsistencies. Furthermore, as in the source-free case considered earlier, all equations of the theory are polynomial in terms of these variables. Therefore, the framework has several potential applications especially to the nonperturbative canonical quantization program.

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