dorsal/arxiv
View SchemaComplex Extension of Quantum Mechanics
| Authors | Carl M. Bender, Dorje C. Brody, Hugh F. Jones |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0208076 |
| URL | https://arxiv.org/abs/quant-ph/0208076 |
| DOI | 10.1103/PhysRevLett.89.270401 |
| Journal | EconfC0306234:617-628,2003; Phys.Rev.Lett.89:270401,2002; Erratum-ibid.92:119902,2004 |
Abstract
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.
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"abstract": "It is shown that the standard formulation of quantum mechanics in terms of\nHermitian Hamiltonians is overly restrictive. A consistent physical theory of\nquantum mechanics can be built on a complex Hamiltonian that is not Hermitian\nbut satisfies the less restrictive and more physical condition of space-time\nreflection symmetry (PT symmetry). Thus, there are infinitely many new\nHamiltonians that one can construct to explain experimental data. One might\nexpect that a quantum theory based on a non-Hermitian Hamiltonian would violate\nunitarity. However, if PT symmetry is not spontaneously broken, it is possible\nto construct a previously unnoticed physical symmetry C of the Hamiltonian.\nUsing C, an inner product is constructed whose associated norm is positive\ndefinite. This construction is completely general and works for any\nPT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is\ngoverned by unitary time evolution. This work is not in conflict with\nconventional quantum mechanics but is rather a complex generalisation of it.",
"arxiv_id": "quant-ph/0208076",
"authors": [
"Carl M. Bender",
"Dorje C. Brody",
"Hugh F. Jones"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1103/PhysRevLett.89.270401",
"journal_ref": "EconfC0306234:617-628,2003; Phys.Rev.Lett.89:270401,2002;\n Erratum-ibid.92:119902,2004",
"title": "Complex Extension of Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0208076"
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