FERMIONIC QUANTUM MECHANICS AND SUPERFIELDS

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Abstract
The explicit forms of consistent eigenstate representations for finite dimensional fermionic quantum theories are considered in detail. In particular are the possible Grassmann characters of the eigenstates determined. A straightforward Schrödinger representation is shown to exist if they are even or odd. For an odd number of real eigenvalues, the eigenstates cannot be even or odd. Still a consistent Schrödinger picture is shown to exist provided the basic canonical operators are antilinearly represented. Since the wave functions within the Schrödinger picture are superfields, the class of superfields which also are first quantized wave functions is determined.

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