On the Spectrum of the Many-Body Pauli Projector

TL;DR

This paper analyzes the spectrum of the many-body Pauli projector, proving a key relation between its kernel and two-body projectors, which informs natural truncation methods in solving many-body quantum systems.

Contribution

It establishes that the kernel of the many-body Pauli projector equals the kernel of the sum of two-body projectors, clarifying the role of many-body Pauli forces.

Findings

Kernel of the many-body projector equals the kernel of two-body projectors sum

Supports truncation of model space based on two-body projectors

Clarifies the role of many-body Pauli forces in multicluster systems

Abstract

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.