Abstract
We study a Schrodinger equation involving a Hamiltonian that is a second-order differential operator, describes free spin-1/2 particles with both energy signs and a definite mass, and depends on a parameterG. One obtains the usual Dirac Hamiltonian by settingG=±i, but for real values ofG the one-particle theory developed here possesses an indefinite metric, so negative energy states have negative normalization. Although the new equation is not manifestly covariant, it is demonstrated that it can be made invariant under proper orthochronous Poincare transformations; it is also invariant under the CPT transformation and charge conjugation, but not, as we interpret it, under space inversion.
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