Knot invariants as nondegenerate quantum geometries

Journal Article · Sun Jan 26 23:00:00 EST 1992 · Physical Review Letters; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.68.431· OSTI ID:5083030

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

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1. Department of Physics, Syracuse University, Syracuse, New York 13244 (United States) Instituto de Fisica, Facultad de Ciencias, Tristan Narvaja 1674, Montevideo (Uruguay) Department of Physics, University of Utah, Salt Lake City, Utah 84112 (United States)

The loop-space representation based on Ashtekar's new variables has allowed for the first time the construction of quantum states of the gravitational field. However, all states known up to the present were associated with spacetime metrics that were everywhere degenerate. In this Letter we present a new exact solution of the constraint equations of quantum gravity that is the first quantum state of the gravitational field known to be associated with a not-everywhere-degenerate metric. The state is associated with the second coefficient of the Alexander-Conway polynomial of knot theory.

• OSTI ID: 5083030
• Journal Information: Physical Review Letters; (United States), Journal Name: Physical Review Letters; (United States) Vol. 68:4; ISSN PRLTA; ISSN 0031-9007
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
661310 -- Relativity & Gravitation-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
FIELD THEORIES
FUNCTIONS
HAMILTONIANS
MATHEMATICAL OPERATORS
MATHEMATICS
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUANTUM OPERATORS
SPACE-TIME
TOPOLOGY
WAVE FUNCTIONS