title: Complex extension of quantum mechanics.
abstract: Requiring that a Hamiltonian be Hermitian is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less restrictive and more physical condition of space-time reflection symmetry (PT symmetry). One might expect a non-Hermitian Hamiltonian to lead to a violation of unitarity. However, if PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry C of the Hamiltonian. Using C, an inner product whose associated norm is positive definite can be constructed. The procedure is general and works for any PT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is governed by unitary time evolution. This work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.
authors.affiliation: Department of Physics, Washington University, St. Louis, MO 63130, USA.
authors.forename: Carl M
authors.initials: CM
authors.lastname: Bender
authors.forename: Dorje C
authors.initials: DC
authors.lastname: Brody
authors.forename: Hugh F
authors.initials: HF
authors.lastname: Jones