2002/08/31 by Carl M. Bender, Dorje C. Brody, Hugh F. Jones · 1 citation
Physics and Astronomy · #quant-ph #hep-th
paper · pdf · doi:10.1103/physrevlett.89.270401
published as EconfC0306234:617-628,2003; Phys.Rev.Lett.89:270401,2002; Erratum-ibid.92:119902,2004 · 4 Pages, Version to appear in PRL
arxiv created 2002/10/30 · arxiv updated 2009/11/30
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians 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). Thus, there are infinitely many new Hamiltonians that one can construct to explain experimental data. One might expect that a quantum theory based on a non-Hermitian Hamiltonian would violate unitarity. However, if PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed physical symmetry C of the Hamiltonian. Using C, an inner product is constructed whose associated norm is positive definite. This construction is completely 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 generalisation of it.