Coherent-state overcompleteness, path integrals, and weak values
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product z z . Because no pair of coherent states is orthogonal, one can represent the closure relation in non-standard ways, in terms of a single p...
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| Autor*in: |
Parisio, Fernando [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Rechteinformationen: |
Nutzungsrecht: © AIP Publishing LLC |
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| Schlagwörter: |
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| Systematik: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of mathematical physics - Melville, NY : American Institute of Physics, 1960, 57(2016), 3, Seite 1 |
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| Übergeordnetes Werk: |
volume:57 ; year:2016 ; number:3 ; pages:1 |
| Links: |
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| DOI / URN: |
10.1063/1.4943014 |
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OLC1972496042 |
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| 520 | |a In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product z z . Because no pair of coherent states is orthogonal, one can represent the closure relation in non-standard ways, in terms of a single phase-space integration of the “unlike” outer product z ′ z , z′≠z. We show that all known representations of this kind have a common ground and that our reasoning extends to spin coherent states. These unlike identities make it possible to write formal expressions for a phase-space path integral, where the role of the Hamiltonian H is played by a weak energy value H w e a k . Therefore, in this context, we can speak of weak values without any mention to measurements. The quantity H w e a k appears as the ruler of the phase-space dynamics in the semiclassical limit. | ||
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10.1063/1.4943014 doi PQ20160430 (DE-627)OLC1972496042 (DE-599)GBVOLC1972496042 (PRQ)a1537-65cedf53c4602ad57774b217df5372e11050151d8cadb84020184b351ef8daec0 (KEY)0000548720160000057000300001coherentstateovercompletenesspathintegralsandweakv DE-627 ger DE-627 rakwb eng 530 510 DNB UA 4660 AVZ rvk Parisio, Fernando verfasserin aut Coherent-state overcompleteness, path integrals, and weak values 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product z z . Because no pair of coherent states is orthogonal, one can represent the closure relation in non-standard ways, in terms of a single phase-space integration of the “unlike” outer product z ′ z , z′≠z. We show that all known representations of this kind have a common ground and that our reasoning extends to spin coherent states. These unlike identities make it possible to write formal expressions for a phase-space path integral, where the role of the Hamiltonian H is played by a weak energy value H w e a k . Therefore, in this context, we can speak of weak values without any mention to measurements. The quantity H w e a k appears as the ruler of the phase-space dynamics in the semiclassical limit. Nutzungsrecht: © AIP Publishing LLC Quantum physics Quantum theory Hilbert space Quantum Physics Enthalten in Journal of mathematical physics Melville, NY : American Institute of Physics, 1960 57(2016), 3, Seite 1 (DE-627)129549703 (DE-600)219135-0 (DE-576)01500290X 0022-2488 nnns volume:57 year:2016 number:3 pages:1 http://dx.doi.org/10.1063/1.4943014 Volltext http://dx.doi.org/10.1063/1.4943014 http://search.proquest.com/docview/1781336208 http://arxiv.org/abs/1403.3033 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 UA 4660 AR 57 2016 3 1 |
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10.1063/1.4943014 doi PQ20160430 (DE-627)OLC1972496042 (DE-599)GBVOLC1972496042 (PRQ)a1537-65cedf53c4602ad57774b217df5372e11050151d8cadb84020184b351ef8daec0 (KEY)0000548720160000057000300001coherentstateovercompletenesspathintegralsandweakv DE-627 ger DE-627 rakwb eng 530 510 DNB UA 4660 AVZ rvk Parisio, Fernando verfasserin aut Coherent-state overcompleteness, path integrals, and weak values 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product z z . Because no pair of coherent states is orthogonal, one can represent the closure relation in non-standard ways, in terms of a single phase-space integration of the “unlike” outer product z ′ z , z′≠z. We show that all known representations of this kind have a common ground and that our reasoning extends to spin coherent states. These unlike identities make it possible to write formal expressions for a phase-space path integral, where the role of the Hamiltonian H is played by a weak energy value H w e a k . Therefore, in this context, we can speak of weak values without any mention to measurements. The quantity H w e a k appears as the ruler of the phase-space dynamics in the semiclassical limit. Nutzungsrecht: © AIP Publishing LLC Quantum physics Quantum theory Hilbert space Quantum Physics Enthalten in Journal of mathematical physics Melville, NY : American Institute of Physics, 1960 57(2016), 3, Seite 1 (DE-627)129549703 (DE-600)219135-0 (DE-576)01500290X 0022-2488 nnns volume:57 year:2016 number:3 pages:1 http://dx.doi.org/10.1063/1.4943014 Volltext http://dx.doi.org/10.1063/1.4943014 http://search.proquest.com/docview/1781336208 http://arxiv.org/abs/1403.3033 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 UA 4660 AR 57 2016 3 1 |
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10.1063/1.4943014 doi PQ20160430 (DE-627)OLC1972496042 (DE-599)GBVOLC1972496042 (PRQ)a1537-65cedf53c4602ad57774b217df5372e11050151d8cadb84020184b351ef8daec0 (KEY)0000548720160000057000300001coherentstateovercompletenesspathintegralsandweakv DE-627 ger DE-627 rakwb eng 530 510 DNB UA 4660 AVZ rvk Parisio, Fernando verfasserin aut Coherent-state overcompleteness, path integrals, and weak values 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product z z . Because no pair of coherent states is orthogonal, one can represent the closure relation in non-standard ways, in terms of a single phase-space integration of the “unlike” outer product z ′ z , z′≠z. We show that all known representations of this kind have a common ground and that our reasoning extends to spin coherent states. These unlike identities make it possible to write formal expressions for a phase-space path integral, where the role of the Hamiltonian H is played by a weak energy value H w e a k . Therefore, in this context, we can speak of weak values without any mention to measurements. The quantity H w e a k appears as the ruler of the phase-space dynamics in the semiclassical limit. Nutzungsrecht: © AIP Publishing LLC Quantum physics Quantum theory Hilbert space Quantum Physics Enthalten in Journal of mathematical physics Melville, NY : American Institute of Physics, 1960 57(2016), 3, Seite 1 (DE-627)129549703 (DE-600)219135-0 (DE-576)01500290X 0022-2488 nnns volume:57 year:2016 number:3 pages:1 http://dx.doi.org/10.1063/1.4943014 Volltext http://dx.doi.org/10.1063/1.4943014 http://search.proquest.com/docview/1781336208 http://arxiv.org/abs/1403.3033 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 UA 4660 AR 57 2016 3 1 |
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10.1063/1.4943014 doi PQ20160430 (DE-627)OLC1972496042 (DE-599)GBVOLC1972496042 (PRQ)a1537-65cedf53c4602ad57774b217df5372e11050151d8cadb84020184b351ef8daec0 (KEY)0000548720160000057000300001coherentstateovercompletenesspathintegralsandweakv DE-627 ger DE-627 rakwb eng 530 510 DNB UA 4660 AVZ rvk Parisio, Fernando verfasserin aut Coherent-state overcompleteness, path integrals, and weak values 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product z z . Because no pair of coherent states is orthogonal, one can represent the closure relation in non-standard ways, in terms of a single phase-space integration of the “unlike” outer product z ′ z , z′≠z. We show that all known representations of this kind have a common ground and that our reasoning extends to spin coherent states. These unlike identities make it possible to write formal expressions for a phase-space path integral, where the role of the Hamiltonian H is played by a weak energy value H w e a k . Therefore, in this context, we can speak of weak values without any mention to measurements. The quantity H w e a k appears as the ruler of the phase-space dynamics in the semiclassical limit. Nutzungsrecht: © AIP Publishing LLC Quantum physics Quantum theory Hilbert space Quantum Physics Enthalten in Journal of mathematical physics Melville, NY : American Institute of Physics, 1960 57(2016), 3, Seite 1 (DE-627)129549703 (DE-600)219135-0 (DE-576)01500290X 0022-2488 nnns volume:57 year:2016 number:3 pages:1 http://dx.doi.org/10.1063/1.4943014 Volltext http://dx.doi.org/10.1063/1.4943014 http://search.proquest.com/docview/1781336208 http://arxiv.org/abs/1403.3033 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_21 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 UA 4660 AR 57 2016 3 1 |
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coherent-state overcompleteness, path integrals, and weak values |
| title_auth |
Coherent-state overcompleteness, path integrals, and weak values |
| abstract |
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product z z . Because no pair of coherent states is orthogonal, one can represent the closure relation in non-standard ways, in terms of a single phase-space integration of the “unlike” outer product z ′ z , z′≠z. We show that all known representations of this kind have a common ground and that our reasoning extends to spin coherent states. These unlike identities make it possible to write formal expressions for a phase-space path integral, where the role of the Hamiltonian H is played by a weak energy value H w e a k . Therefore, in this context, we can speak of weak values without any mention to measurements. The quantity H w e a k appears as the ruler of the phase-space dynamics in the semiclassical limit. |
| abstractGer |
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product z z . Because no pair of coherent states is orthogonal, one can represent the closure relation in non-standard ways, in terms of a single phase-space integration of the “unlike” outer product z ′ z , z′≠z. We show that all known representations of this kind have a common ground and that our reasoning extends to spin coherent states. These unlike identities make it possible to write formal expressions for a phase-space path integral, where the role of the Hamiltonian H is played by a weak energy value H w e a k . Therefore, in this context, we can speak of weak values without any mention to measurements. The quantity H w e a k appears as the ruler of the phase-space dynamics in the semiclassical limit. |
| abstract_unstemmed |
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product z z . Because no pair of coherent states is orthogonal, one can represent the closure relation in non-standard ways, in terms of a single phase-space integration of the “unlike” outer product z ′ z , z′≠z. We show that all known representations of this kind have a common ground and that our reasoning extends to spin coherent states. These unlike identities make it possible to write formal expressions for a phase-space path integral, where the role of the Hamiltonian H is played by a weak energy value H w e a k . Therefore, in this context, we can speak of weak values without any mention to measurements. The quantity H w e a k appears as the ruler of the phase-space dynamics in the semiclassical limit. |
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| title_short |
Coherent-state overcompleteness, path integrals, and weak values |
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