AT4 - Geometric Calculus in Gravity Theory |
Speaker_ |
Nester, James M |
Talk _ |
On the zeros of spinor fields and an orthonormal frame gauge |
Abstract _ |
We had 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 & 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. But 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. |