Quantum action principle and base operators for bosons and fermions

Abstract

A new quantum action principle is formulated by expressing the Klein–Gordon, Dirac and Proca equations in the form of eigenvalue equations for quantum action operators. These operators are Hermitian and they become the base operators for bosons and fermions. The principle postulates that their only allowed eigenvalue is Planck's constant. Relationships between the quantum action operators and the Casimir operators of the Poincaré group and translation group are derived. It is shown that the obtained results supplement Wigner's original work on classification of the irreducible representations of the Poincaré group.