On the spectrum of the many-body Pauli projector

Spectrum of the Pauli projector of a quantum many-body system is studied using the methods of operator algebra. It is proven that the kernel of the complete many-body projector is identical to the kernel of the sum of two-body projectors. Since the kernel 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 of solving the Schrodinger equation for the many-body system. These relations clarify the role of many-body Pauli forces in a multicluster system.