Fermionic Wave Functions on Unordered Configurations

Understand

Quantum mechanical wave functions of N identical fermions are usually represented as anti-symmetric functions of ordered configurations.

• Leinaas and Myrheim proposed how a fermionic wave function can be represented as a function of unordered configurations, which is desirable as the ordering is artificial and unphysical.
• In this approach, the wave function is a cross-section of a particular Hermitian vector bundle over the configuration space, which we call the fermionic line bundle.
• Here, we provide a justification for Leinaas and Myrheim's proposal, that is, a justification for regarding cross-sections of the fermionic line bundle as equivalent to anti-symmetric functions of ordered configurations.