- 03-416 Dr Lee McCulloch-James
- Symplectic structures and two spinor chiral formulations
of Einstein-matter Lagrangians.
Sep 12, 03
(auto. generated ps),
of related papers
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.