New variables for gravity: Inclusion of matter

Abhay Ashtekar, Joseph D. Romano, Ranjeet S. Tate

Research output: Contribution to journalArticle

134 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2572-2587
Number of pages16
JournalPhysical Review D
Volume40
Issue number8
DOIs
StatePublished - Jan 1 1989

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All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

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