Witten identities for rotations, spinor boundary-value problems and new gauge conditions for asymptotic symmetries

Physics

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Boundary Value Problems, Gravitation Theory, Relativity, Spin Dynamics, Spinor Groups, Unified Field Theory, Angular Momentum, Asymptotic Methods, Rotation, Space-Time Functions, Symmetry

Scientific paper

The construction of measures of energy-momentum and angular momentum using spinor methods is considered in the theory of linearized gravitation and in general relativity. A new measure of angular momentum is obtained by generalizing Witten's identities for energy-momentum, and at null infinity, for the appropriate choice of Poincare group, agreement with Penrose's quasi-local expression is obtained. The expressions introduced here may be regarded as a form of the linkage expression given by Geroch and Winicour, but with a new choice of the gauge conditions for asymptotic symmetries. The methods introduced here can also be applied quasi-locally and some simple examples are given.

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