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1
2
up with the spin. Yet the (-1) which seems to play an essential role in the quantization of
fermion fields has no evident connection with spin. It will take a careful analysis of quantum
1
2
electrodynamics to resolve this apparent conflict. Again, the tie up of (-1) and spin
suggests that analytic continuation of scattering amplitudes cannot be properly understood
without taking spin into account.13 On the other hand, there may be geometrically different
kinds of analytic continuation, for there are several different geometical roots of minus one
in the Dirac algebra.
13
A formulation of the  complex Lorentz group in terms of the real Dirac algebra is given
in Sec. 19 of Ref. 2.
18
Anyone who plays the game of theoretical physics with the rules suggested here will not
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allow a (-1) in his theory unless it has a geometrical significance grounded in space-time.
This may be regarded as another constraint imposed by space-time on permissible physical
equations which had already been restricted by the requirement of relativistic covariance
or invariance.
We have exhihited several bilinear  observables of a spinor field È. The Dirac theory
supplies a physical interpretation of J0 = ȳ0È and of the general orientation of the frame
{Ji = ȳiÈ}. We have suggested an interpretation of ÈÈ which awaits final justification.
To supply a more detailed interpretation of the Jµ, we must go well beyond the Dirac
theory. This possibility will be explored in another paper.
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