On the Spectrum of the Many-Body Pauli Projector

Spectrum of the Pauli projector of a quantum many-body system is studied. It is proven that the kern of the complete many-body projector is identical to the kern of the sum of two-body projectors. Since the kern of the many-body Pauli projector defines an allowed subspace of the complete Hilbert space, it is argued that a truncation of the many-body model space following the two-body Pauli projectors is a natural way when solving the Schr"{o}dinger equation for the many-body system. These relations clarify a role of the many-body Pauli forces in a multicluster system.

💡 Research Summary

The paper investigates the spectral properties of the Pauli projector in quantum many‑body systems and establishes a rigorous relationship between the full many‑body projector and the sum of two‑body projectors. In the conventional treatment of fermionic systems, the Pauli principle is enforced by constructing a projector that eliminates any component of the wave function in which two particles occupy the same quantum state. For an N‑particle system one can define a two‑body projector (P_{ij}) for each unordered pair ((i,j)). The full many‑body projector is often written as a product
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