The graph-representation approach to topological field theory in 2 + 1 dimensions

Journal Article · Thu Jan 30 00:00:00 EST 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92000259· OSTI ID:5368382

Martin, S P ^[1]

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1. Florida Univ., Gainesville, FL (United States). Dept. of Physics

In this paper an alternative definition of topological quantum field theory in 2 + 1 dimensions is discussed. The fundamental objects in this approach are not gauge fields as in the usual approach, but nonlocal observables associated with graphs. The classical theory of graphs is defined by postulating a simple diagrammatic rule for computing the Poisson bracket of any two graphs. The theory is quantized by exhibiting a quantum deformation of the classical Poisson-bracket algebra, which is realized as a commutator algebra on a Hilbert space of states. The wave functions in this graph representation approach are functionals on an appropriate set of graphs. This is in contrast to the usual connection representation approach, in which the theory is defined in therms of a gauge field and the wave functions are functionals on the space of flat spatial connections modulo gauge transformations.

• OSTI ID: 5368382
• Journal Information: International Journal of Modern Physics A; (United States), Vol. 7:3; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
POISSON EQUATION
CLASSICAL MECHANICS
COMMUTATORS
DIAGRAMS
FIELD ALGEBRA
FUNCTIONALS
GAUGE INVARIANCE
HILBERT SPACE
QUANTIZATION
THREE-DIMENSIONAL CALCULATIONS
TOPOLOGY
TRANSFORMATIONS
WAVE FUNCTIONS
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SPACE
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)