Yang-Mills theory and general relativity in three and four dimensions

Details Yang-Mills theory and general relativity in three and four dimensions Yang-Mills theory and general relativity in three and four dimensions

Mar 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phlb..220...51b&link_type=abstract

Physics Letters B, Volume 220, Issue 1-2, p. 51-54.

Physics

28

Scientific paper

Ashtekar has shown that general relativity can be ``embedded'' in the phase space of a Yang-Mills theory with a rank one gauge algebra, provided that the dimension of space is three. Witten has given a similar construction, valid when the dimension of space is two. In this letter we show how these two results are related to each other. In fact, Ashtekar's formulation works also in the lower dimension, and it is equivalent to Witten's formulation as long as the spatial metric is non-degenerate. We explain why a simplified constraint algebra appears in the latter case.

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