Topological limit of gravity admitting an SU(2) connection formulation
- Centre de Physique Theorique, Campus de Luminy, 13288 Marseille (France)
We study the Hamiltonian formulation of the generally covariant theory defined by the Lagrangian 4-form L=e{sub I} and e{sub J} and F{sup IJ}({omega}), where e{sup I} is a tetrad field and F{sup IJ} is the curvature of a Lorentz connection {omega}{sup IJ}. This theory can be thought of as the limit of the Holst action for gravity for the Newton constant G{yields}{infinity} and Immirzi parameter {gamma}{yields}0, while keeping the product G{gamma} fixed. This theory has for a long time been conjectured to be topological. We prove this statement both in the covariant phase space formulation as well as in the standard Dirac formulation. In the time gauge, the unconstrained phase space of theory admits an SU(2) connection formulation which makes it isomorphic to the unconstrained phase space of gravity in terms of Ashtekar-Barbero variables. Among possible physical applications, we argue that the quantization of this topological theory might shed new light on the nature of the degrees of freedom that are responsible for black entropy in loop quantum gravity.
- OSTI ID:
- 21409415
- Journal Information:
- Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 6 Vol. 81; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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DEGREES OF FREEDOM
ENTROPY
FIELD THEORIES
FUNCTIONS
GRAVITATION
HAMILTONIANS
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
PHASE SPACE
PHYSICAL PROPERTIES
QUANTIZATION
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUANTUM OPERATORS
SPACE
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
THERMODYNAMIC PROPERTIES
TOPOLOGY