Extended loop representation of quantum gravity
- Departamento de Fisica, Universidad Simon Bolivar, Apartado 89000, Caracas 1080-A (Venezuela)
- Instituto de Fisica, Facultad de Ciencias, Tristan Narvaja 1674, Montevideo (Uruguay)
A new representation of quantum gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group that we call the extended loop group behaves locally as an infinite dimensional Lie group. Quantum gravity can be realized on the state space of extended loop-dependent wave functions. The extended representation generalizes the loop representation and contains this representation as a particular case. The resulting diffeomorphism and Hamiltonian constraints take a very simple form and allow us to apply functional methods and simplify the loop calculus. In particular we show that the constraints are linear in the momenta. The nondegenerate solutions known in the loop representation are also solutions of the constraints in the new representation. An approach to the regularization problems associated with the formal calculus is performed. We show that the solutions are generalized knot invariants, smooth in the extended variables, and any framing is unnecessary.
- OSTI ID:
- 6644481
- Journal Information:
- Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 51:2; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONSTRAINTS
DISPERSIONS
FIELD THEORIES
FUNCTIONALS
FUNCTIONS
GAUGE INVARIANCE
HAMILTONIANS
INVARIANCE PRINCIPLES
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL OPERATORS
MIXTURES
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUANTUM OPERATORS
SOLUTIONS
SYMMETRY GROUPS
WAVE FUNCTIONS