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

Journal Article · Thu Jan 30 04:00:00 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), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:3; ISSN IMPAE; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

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