Complex Extension of Quantum Mechanics

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dc.creatorBender, Carl M.
dc.creatorBrody, Dorje C.
dc.creatorJones, Hugh F.
dc.date2002-08-12
dc.date2002-10-30
dc.date.accessioned2026-07-07T12:17:07Z
dc.date.available2026-07-07T12:17:07Z
dc.descriptionIt 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.
dc.description4 Pages, Version to appear in PRL
dc.identifierhttps://arxiv.org/abs/quant-ph/0208076
dc.identifierhttp://arxiv.org/abs/quant-ph/0208076
dc.identifierEconfC0306234:617-628,2003; Phys.Rev.Lett.89:270401,2002; Erratum-ibid.92:119902,2004
dc.identifierdoi:10.1103/PhysRevLett.89.270401
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212013
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.titleComplex Extension of Quantum Mechanics
dc.typetext

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