03-416 Dr Lee McCulloch-James

Symplectic structures and two spinor chiral formulations of Einstein-matter Lagrangians. (64K, AMS-Latex) Sep 12, 03

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Abstract. Equivalent chiral Lagrangians for (complex) Einstein equations are collected and related by their identical (infinite dimensional) (pre)symplectic structures. Viewing Plebanski's Lagrangian that employs an $sl(2,C)$-valued field variable alternative to the tetrad as a constrained BF theory, extensions to other (super) gauge groups follow naturally. Accordingly, scalar and spinor matter field couplings to an Einstein-Maxwell Lagrangian employing $gl(2,C)$-valued (spinor desnity)field variables are derived. Usiing instead, spin $\thalf$ fields as dynamical variables and symplectic techniques a succinct derivation of the Witten-Nester two-form as a Noether charge is realised.

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