Self duality and quantization

Abhay Ashtekar, Carlo Rovelli, Lee Smolin

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The quantum theory of the free Maxwell field in Minkowski space is constructed using a representation in which the self dual connection is diagonal. Quantum states are now holomorphic functionals of self dual connections and a decomposition of fields into positive and negative frequency parts is unnecessary. The construction requires the introduction of new mathematical techniques involving "holomorphic distributions". The method extends also to linear gravitons in Minkowski space. The fact that one can recover the entire Fock space - with particles of both helicities - from self dual connections alone provides independent support for a non-perturbative, canonical quantization program for full general relativity based on self dual variables.

Original languageEnglish (US)
Pages (from-to)7-27
Number of pages21
JournalJournal of Geometry and Physics
Issue number1-4
StatePublished - Mar 1992

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology


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