Worldsheet formulations of gauge theories and gravity

Abstract

The evolution operator for states of gauge theories in the graph representation (closely related to the loop representation of Gambini and Trias, and Rovelli and Smolin) is formulated as a weighted sum over worldsheets interpolating between initial and final graphs. As examples, lattice $SU(2)$ BF and Yang-Mills theories are expressed as worldsheet theories, and (formal) worldsheet forms of several continuum $U(1)$ theories are given. It is argued that the world sheet framework should be ideal for representing GR, at least euclidean GR, in 4 dimensions, because it is adapted to both the 4-diffeomorphism invariance of GR, and the discreteness of 3-geometry found in the loop representation quantization of the theory. However, the weighting of worldsheets in GR has not yet been found.

arXiv commentExpanded version of talk given at the 7th Marcel Grossmann Meeting Stanford, July 94. Gives results obtained + sketches of derivations - does not give all proofs. Latex 20 pages, 8 uuencoded postscript figures. Uses macro psfig.tex available from this archive (and appended to this posting for you convenience). After latexing use dvips -not- dvi2ps to get postscript file

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