New variables for gravity: Inclusion of matter

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

Research output: Contribution to journalArticlepeer-review

139 Scopus citations


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
Pages (from-to)2572-2587
Number of pages16
JournalPhysical Review D
Issue number8
StatePublished - 1989


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