A combinatorial approach to diffeomorphism invariant quantum gauge theories

Journal Article · Sat Nov 01 04:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532159· OSTI ID:553988

Zapata, J A ^[1]

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1. Center for Gravitational Physics and Geometry, Department of Physics, The Pennsylvania State University, 104 Davey Laboratory, University Park, Pennsylvania 16802 (United States)

Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical states are gauge and diffeomorphism invariant distributions on the space of functions of the holonomies of the edges of a certain family of graphs. Then a family of graphs embedded in the space manifold (satisfying certain properties) induces a representation of the algebra of physical observables. We construct a quantum model from the set of piecewise linear graphs on a piecewise linear manifold, and another manifestly combinatorial model from graphs defined on a sequence of increasingly refined simplicial complexes. Even though the two models are different at the kinematical level, they provide unitarily equivalent representations of the algebra of physical observables in {ital separable} Hilbert spaces of physical states (their s-knot basis is countable). Hence, the combinatorial framework is compatible with the usual interpretation of quantum field theory. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 553988
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGEBRA
HILBERT SPACE
MATHEMATICAL MANIFOLDS
QUANTUM FIELD THEORY
UNIFIED GAUGE MODELS
UNITARITY