Form Curve Metric

Double check my proof?
I've just solved a curved spacetime wavefunction with hermitian matrices for an explicitly covariant form of feynman's slash notation. If the energy per oscillator is correct the pseudo-orthogonal 4-d space with metric signature (+ - - -) should fold and form a tube like consistancy in spacetime. Does anyone see any problems with this? I'm sure someone will mention multiplying (- + + +) by a factor of i but this is only necessary if the we use the conjugate transpose of £.
Thanks for you help!
Daaaaaaaaang
you right.
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