2003/03/21 by Carl M. Bender, Dorje C. Brody, Hugh F. Jones · 11 citations
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Canonical quantization #Covariant Hamiltonian field theory #Hamiltonian (control theory) #Hamiltonian mechanics #Observable #Physical system #Quantization (signal processing) #Quantum #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Reflection symmetry #Unitary state #hep-th
paper · pdf · doi:10.1119/1.1574043
published as Am.J.Phys. 71 (2003) 1095-1102 · Revised version to appear in American Journal of Physics
arxiv created 2003/03/21 · openalex publication_date 2003/10/13 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space–time reflection symmetry (𝒫𝒯 symmetry). Thus, there are infinitely many new Hamiltonians that one can construct that might explain experimental data. One would think that a quantum theory based on a non-Hermitian Hamiltonian violates unitarity. However, if 𝒫𝒯 symmetry is not broken, it is possible to use a previously unnoticed physical symmetry of the Hamiltonian to construct an inner product whose associated norm is positive definite. This construction is general and works for any 𝒫𝒯-symmetric Hamiltonian. The dynamics is governed by unitary time evolution. This formulation does not conflict with the requirements of conventional quantum mechanics. There are many possible observable and experimental consequences of extending quantum mechanics into the complex domain, both in particle physics and in solid state physics.