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Quantum mechanical wave functions of N identical fermions are usuallyrepresented as anti-symmetric functions of ordered configurations. Leinaas andMyrheim proposed how a fermionic wave function can be represented as a functionof unordered configurations, which is desirable as the ordering is artificialand unphysical. In this approach, the wave function is a cross-section of aparticular Hermitian vector bundle over the configuration space, which we callthe fermionic line bundle. Here, we provide a justification for Leinaas andMyrheim's proposal, that is, a justification for regarding cross-sections ofthe fermionic line bundle as equivalent to anti-symmetric functions of orderedconfigurations. In fact, we propose a general notion of equivalence of twoquantum theories on the same configuration space; it is based on specifying aquantum theory as a triple $(\mathscr{H},H,Q)$ (``quantum triple'') consistingof a Hilbert space $\mathscr{H}$, a Hamiltonian $H$, and a family of positionoperators (technically, a projection-valued measure on configuration spaceacting on $\mathscr{H}$).

Fermionic Wave Functions on Unordered Configurations