How the Jones polynomial give rise to physical states of quantum general relativity

Journal Article · Fri Jan 01 00:00:00 EST 1993 · General Relativity and Gravitation; (United States)

DOI:https://doi.org/10.1007/BF00756923· OSTI ID:6647032

Bruegmann, B ^[1]; Gambini, R ^[2]; Pullin, J ^[3]

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1. Syracuse Univ., NY (United States)
2. Facultad de Ciencias, Montevideo (Uruguay)
3. Univ. of Utah, Salt Lake City (United States)

Solutions to both the diffeomorphism and the hamiltonian constraint of quantum gravity have been found in the loop representation, which is based on Ashtekar's new variables. While the diffeomorphism constraint is easily solved by considering loop functionals which are knot invariants, there remains the puzzle why several of the known knot invariants are also solutions to the hamiltonian constraint. We show how the Jones polynomial gives rise to an infinite set of solutions to all the constraints of quantum gravity thereby illuminating the structure of the space of solutions and suggesting the existence of a deep connection between quantum gravity and knot theory at a dynamical level.

• OSTI ID: 6647032
• Journal Information: General Relativity and Gravitation; (United States), Vol. 25:1; ISSN 0001-7701
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GENERAL RELATIVITY THEORY
EQUATIONS
QUANTUM GRAVITY
ANALYTIC FUNCTIONS
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONALS
HAMILTONIANS
POLYNOMIALS
SPACE-TIME
WAVE FUNCTIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICAL OPERATORS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
661310* - Relativity & Gravitation- (1992-)