Dynamical groups of parametrized systems: Atomic supermultiplets

Abstract

Lie groups that allow transformation of parameters in a Hamiltonian are investigated. Stability considerations suggest treating the parameters as dynamical variables. This yields generalized Hamiltonian systems in an enlarged classical phase space, and “third quantized” Hamiltonians in quantum mechanics. These proved a conceptually and mathematically convenient tool for uncovering relationships between the properties of related physical systems.