On the "equivalence" of the Maxwell and Dirac equations

Details On the "equivalence" of the Maxwell and Dirac equations On the "equivalence" of the Maxwell and Dirac equations

2002-01-25

arxiv.org/abs/math-ph/0201053v2

Published in Int. J. Theor. Phys., Vol.41 (April 2002) 689--694

Physics

Mathematical Physics

8 pages, final version with minor corrections and additional references

Scientific paper

It is shown that Maxwell's equation cannot be put into a spinor form that is equivalent to Dirac's equation. First of all, the spinor \psi in the representation \vec{F} = \psi \vec{u} \bar{\psi} of the electromagnetic field bivector depends on only three independent complex components whereas the Dirac spinor depends on four. Second, Dirac's equation implies a complex structure specific to spin 1/2 particles that has no counterpart in Maxwell's equation. This complex structure makes fermions essentially different from bosons and therefore insures that there is no physically meaningful way to transform Maxwell's and Dirac's equations into each other.

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