[time 62] Should Metric Signature Matter in Clifford Algebra Formulations

Stephen P. King (stephenk1@home.com)
Sat, 27 Mar 1999 08:47:22 -0500

Hi all,

        For all Clifford algebra fans! :)

"Standard formulation is unable to distinguish between the (+++-) and
(---+) spacetime metric signatures.
     However, the Clifford algebras associated with each are
inequivalent, R(4) in the first case (real 4 by 4 matrices), H(2) in the
latter (quaternionic 2 by 2). Multivector reformulations of Dirac theory
by various authors look quite inequivalent pending the algebra assumed.
It is not clear if this is mere artifact, or if there is a right/wrong
choice as to which one describes reality. However, recently it has been
shown that one can map from one signature to the other using a "tilt
transformation" [see P. Lounesto, "Clifford Algebras and Hestenes
Spinors", Found. Phys. 23, 1203-1237 (1993)]. The broader question is
that if the universe is signature blind, then perhaps a complete theory
should be manifestly tilt covariant. A generalized multivector wave
equation is proposed which is fully signature invariant in form, because
it includes all the components of the algebra in the wavefunction
(instead of restricting it to half) as well as all the possibilities for
interaction terms."


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