Should symmetric quantum mechanics be interpreted as nonlinear?

Abstract

The Feshbach-type reduction of the Hilbert space to the physically most relevant “model” subspace is suggested as a means of a formal unification of the standard quantum mechanics with its recently proposed (Formula presented.) symmetric modification. The resulting “effective” Hamiltonians H eff(E) are always Hermitian, and the two alternative forms of their energy-dependence are interpreted as a certain dynamical nonlinearity, responsible for the repulsion and/or attraction of the levels in the Hermitian and/or (Formula presented.) symmetric cases, respectively. The spontaneous (Formula presented.) symmetry breaking is then reflected by the loss of the Hermiticity of H eff while the pseudo-unitary evolution law persists in the unreduced Hilbert space. © 2002 Taylor & Francis Group, LLC.