Reformulation of the Hamiltonian constraint of four-dimensional gravity for arbitrary values of the Immirzi parameter via the affine group formalism
Year: 2013
Type: article
Abstract: One of the virtues of the Ashtekar variables is the simplification of the initial value constraints for gravity. In the case of self-dual variables this entails a complexification of the phase space which comes at the expense of having to implement reality conditions in the Lorentzian signature case. A reformulation of the theory in terms of real variables eliminates this difficulty, albeit at the expense of having to deal with a more complicated Hamiltonian constraint. The set of available gravitational theories classically equivalent to Einstein's is parametrized by a parameter $β$, known as the Immirzi parameter. We rephrase the Hamiltonian constraint into the form of an affine Lie algebra for arbitrary $β$, and perform a quantization.
Source: Classical and Quantum Gravity
Author: Eyo Eyo Ita
Institution: United States Naval Academy
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1983315092