Decomposition Theorem for Density Operators of a Pure Quantum State

摘要

Conditions for the existence of a decomposition of a hermitian projector rho into two hermitian and time reversal invariant operators r/rho sub 0 and chi under the form rho=e/sup i,chi/rho sub 0 e/sup -i,chi/ are investigated. Sufficient conditions are given, and an explicit construction of a decomposition is performed when they are fulfilled. A stronger theorem of existence and unicity is studied. All the proofs are valid for any p-body reduced density operator of a pure state of a system of bosons as well as fermions. The decomposition studied in this work has already been used in Nuclear Physics, and may be of interest in other fields of Physics. (Atomindex citation 11:520157)