Reality conditions for Ashtekar variables as Dirac constraints

1996/07/21 by Hugo A. Morales-Tecotl, H. A. Morales-Técotl, Luis F. Urrutia +1 · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/13/11/009

published as Class.Quant.Grav. 13 (1996) 2933-2940 · 16 pages, plain LaTeX, submitted to Class. Quant. Grav. E-mail: [email protected]

arxiv created 1996/07/21 · openalex publication_date 1996/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We show that the reality conditions to be imposed on Ashtekar variables to recover real gravity can be implemented as second-class constraints following Dirac. Thus, counting gravitational degrees of freedom follows accordingly. Some constraints of the real theory turn out to be non-polynomial, regardless of the form, polynomial or non-polynomial, taken for the reality conditions. We comment upon the compatibility of our approach with the recently proposed Wick transform point of view, as well as on some alternatives for dealing with such second-class constraints.

Citations

• Quantization of Gauge Systems
• Bibliography of Publications related to Classical and Quantum Gravity in terms of the Ashtekar Variables

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