On the Zeros of Spinor Fields and AN Orthonormal Frame Gauge Condition

Details On the Zeros of Spinor Fields and AN Orthonormal Frame Gauge Condition On the Zeros of Spinor Fields and AN Orthonormal Frame Gauge Condition

Sep 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008mgm..conf.1332n&link_type=abstract

"THE ELEVENTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation an

Physics

2

Spinor Zeros, Special Orthonormal Frame

Scientific paper

We proposed (in connection with a positive energy proof/localization) certain rotational gauge conditions for a preferred orthonormal frame on a Riemannian manifold. For certain physically interesting cases (dimensions 2, 3 and 4) such frames can be constructed from spinors (regarded as rotation-dilations) which solve the Dirac or Witten equations--with the important exception of points at which the spinor field vanishes. Are such zero points a serious problem? Here, using explicit examples, we show that spinor zeros really can happen. However we also argue that solutions with zeros are quite exceptional; for generic metrics and boundary data there are no zeros. We conclude that the "special orthonormal frame" gauge conditions can be used essentially without reservations.

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