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Gauge choice in Witten's energy expression

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Witten's equation\(\not D\psi = 0\) can be interpreted as a gauge fixing condition for classical supergravity. We rigorously prove the existence of asymptotically constant solutions of the more general gauge condition\(\not D\psi = A\psi\) for almost all endomorphismsA of the spin bundle. Each gives an expression for the gravitational energy similar to Witten's. These include the choice\(A = \sqrt R\), which yields the particularly elegant energy expression first noticed by Deser.

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Authors and Affiliations

  1. Department of Mathematics, Brandeis University, 02154, Waltham, MA, USA

    Thomas H. Parker

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  1. Thomas H. Parker
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Communicated by A. Jaffe

Partially supported by N. S. F. Grant MCS-82-02018 at Harvard University

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Parker, T.H. Gauge choice in Witten's energy expression. Commun.Math. Phys. 100, 471–480 (1985). https://doi.org/10.1007/BF01217725

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  • DOI: https://doi.org/10.1007/BF01217725

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