Symmetry Equivalents of the Weak Value Measurement Pointer Hamiltonian

Abstract

Quantum mechanical weak values and their measurement have been a focus of theoretical, experimental, and applied research for more than two decades. The concept of PT symmetry was also introduced into quantum mechanics during this time. This paper defines the notion of a weak value measurement pointer Hamiltonian and establishes equivalences between its Dirac symmetries, its PT symmetries, its eigenvalues, and the associated weak value. The affect of these symmetries upon measurement pointer observables is also identified.