Complex conformal rescalings and complex Lorentz transformations.

Details Complex conformal rescalings and complex Lorentz transformations. Complex conformal rescalings and complex Lorentz transformations.

Jan 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987gregr..19....1l&link_type=abstract

General Relativity and Gravitation, Volume 19, Issue 1, pp.1-21

Computer Science

2

Gravitation Theory:Space-Time

Scientific paper

Complex Lorentz transformations and complex conformal rescalings with independent conformal factorsθ andtilde θ are investigated in terms of elements of the group GL(2,C) ⊗ G{tilde L}(2,C). It is shown how a general element of this group decomposes into a “standard” conformal rescaling (withtilde θ =θ), a “pure spin transformation,” complex null rotations, and a complex boost-rotation. Of particular interest are the pure spin transformations that leave invariant the metric but transform the permutation spinors. It is these transformations that, whentilde θ ≡θ, are responsible for seemingly complicating the transformation law of the derivative operator and of spinors dependent thereon. It has been suggested that to avoid this complication one should allow the rescaled metric to have torsion. It is argued here that simplicity can be achieved even when the torsion-free condition is imposed.

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