Two dimensional general covariance from three dimensions

Details Two dimensional general covariance from three dimensions Two dimensional general covariance from three dimensions

1993-05-03

arxiv.org/abs/hep-th/9305006v1

Class.Quant.Grav.10:L93-L100,1993

Physics

High Energy Physics

High Energy Physics - Theory

10 pages (Latex), Alberta-Thy-19-93

Scientific paper

10.1088/0264-9381/10/8/002

A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of conserved charges that are associated with graphs in two dimensions and the Poisson algebra of the charges is closed. For 2-manifolds with boundary there are additional observables that have a Kac-Moody Poisson algebra. It is further shown that the theory is classically integrable and the general solution of the equations of motion is given. The quantum theory is described using Dirac quantization, and it is shown that there are quantum states associated with graphs in two dimensions.

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