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Instanton representation of Plebanski gravity. The classical theory. (English) Zbl 1323.83003

Summary: This paper is a self-contained introduction to the instanton representation of Plebanski gravity (IRPG), a formulation of General Relativity (GR) where the basic variables are a spacetime gauge connection and a three by three matrix valued in the Lie algebra of \(\mathfrak{so}(3,\mathbb{C})\). We present a classical analysis of the IRPG from various perspectives, noting some of its interesting features and motivations.

MSC:

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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