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Title: Gravitational Dynamics—A Novel Shift in the Hamiltonian Paradigm
Authors: Ashtekar, Abhay
Varadarajan, Madhavan
Keywords: general relativity dynamics;
gauge theory
hamiltonian framework
Issue Date: Feb-2021
Publisher: (MDPI)- Molecular Diversity Preservation International
Citation: Universe 2021, Vol.7, Iss. 1, 13.
Abstract: It is well known that Einstein’s equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that time evolution of the gravitational field can be re-expressed as (a gauge covariant generalization of) the Lie derivative along a novel shift vector field in spatial directions. Thus, the canonical transformation enerated by the Hamiltonian constraint acquires a geometrical interpretation on the Yang-Mills phase space, similar to that generated by the diffeomorphism constraint. In classical general relativity this geometrical interpretation significantly simplifies calculations and also illuminates the relation between dynamics in the ‘integrable’ (anti)self-dual sector and in the full theory. For quantum gravity, it provides a point of departure to complete the Dirac quantization program for general relativity in a more satisfactory fashion. This gauge theory perspective may also be helpful in extending the ‘double copy’ ideas relating the Einstein and Yang-Mills dynamics to a non-perturbative regime. Finally, the notion of generalized, gauge covariant Lie derivative may also be of interest to the mathematical physics community as it hints at some potentially rich structures that have not been explored.
Description: Open Access
ISSN: 2218-1997
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Copyright: © 2021 by the authors. Licensee MDPI
Appears in Collections:Research Papers (TP)

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