Geometry, Topology and Quantization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1996
|
| Schriftenreihe: | Mathematics and Its Applications
386 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quantization. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamiltonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as proposed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direction vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit |
| Beschreibung: | 1 Online-Ressource (X, 230 p) |
| ISBN: | 9789401154260 9789401062824 |
| DOI: | 10.1007/978-94-011-5426-0 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423982 | ||
| 003 | DE-604 | ||
| 005 | 20170919 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1996 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401154260 |c Online |9 978-94-011-5426-0 | ||
| 020 | |a 9789401062824 |c Print |9 978-94-010-6282-4 | ||
| 024 | 7 | |a 10.1007/978-94-011-5426-0 |2 doi | |
| 035 | |a (OCoLC)1165541386 | ||
| 035 | |a (DE-599)BVBBV042423982 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 530.1 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Bandyopadhyay, Pratul |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometry, Topology and Quantization |c by Pratul Bandyopadhyay |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 1996 | |
| 300 | |a 1 Online-Ressource (X, 230 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and Its Applications |v 386 | |
| 500 | |a This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quantization. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamiltonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as proposed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direction vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit | ||
| 650 | 4 | |a Physics | |
| 650 | 4 | |a Global differential geometry | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Nuclear physics | |
| 650 | 4 | |a Theoretical, Mathematical and Computational Physics | |
| 650 | 4 | |a Quantum Physics | |
| 650 | 4 | |a Elementary Particles, Quantum Field Theory | |
| 650 | 4 | |a Nuclear Physics, Heavy Ions, Hadrons | |
| 650 | 4 | |a Differential Geometry | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 0 | 7 | |a Geometrische Quantisierung |0 (DE-588)4156720-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Geometrische Quantisierung |0 (DE-588)4156720-1 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 830 | 0 | |a Mathematics and Its Applications |v 386 |w (DE-604)BV008163334 |9 386 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-011-5426-0 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859399 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153100386172928 |
|---|---|
| any_adam_object | |
| author | Bandyopadhyay, Pratul |
| author_facet | Bandyopadhyay, Pratul |
| author_role | aut |
| author_sort | Bandyopadhyay, Pratul |
| author_variant | p b pb |
| building | Verbundindex |
| bvnumber | BV042423982 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165541386 (DE-599)BVBBV042423982 |
| dewey-full | 530.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1 |
| dewey-search | 530.1 |
| dewey-sort | 3530.1 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-94-011-5426-0 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03443nmm a2200541zcb4500</leader><controlfield tag="001">BV042423982</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20170919 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1996 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401154260</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-011-5426-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401062824</subfield><subfield code="c">Print</subfield><subfield code="9">978-94-010-6282-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-011-5426-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1165541386</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423982</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">530.1</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bandyopadhyay, Pratul</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Geometry, Topology and Quantization</subfield><subfield code="c">by Pratul Bandyopadhyay</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (X, 230 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">386</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quantization. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamiltonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as proposed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direction vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global differential geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quantum theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nuclear physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Theoretical, Mathematical and Computational Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quantum Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Elementary Particles, Quantum Field Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nuclear Physics, Heavy Ions, Hadrons</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quantentheorie</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrische Quantisierung</subfield><subfield code="0">(DE-588)4156720-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Geometrische Quantisierung</subfield><subfield code="0">(DE-588)4156720-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">386</subfield><subfield code="w">(DE-604)BV008163334</subfield><subfield code="9">386</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-011-5426-0</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859399</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042423982 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401154260 9789401062824 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859399 |
| oclc_num | 1165541386 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (X, 230 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer Netherlands |
| record_format | marc |
| series | Mathematics and Its Applications |
| series2 | Mathematics and Its Applications |
| spelling | Bandyopadhyay, Pratul Verfasser aut Geometry, Topology and Quantization by Pratul Bandyopadhyay Dordrecht Springer Netherlands 1996 1 Online-Ressource (X, 230 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 386 This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quantization. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamiltonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as proposed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direction vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit Physics Global differential geometry Quantum theory Nuclear physics Theoretical, Mathematical and Computational Physics Quantum Physics Elementary Particles, Quantum Field Theory Nuclear Physics, Heavy Ions, Hadrons Differential Geometry Quantentheorie Geometrische Quantisierung (DE-588)4156720-1 gnd rswk-swf Geometrische Quantisierung (DE-588)4156720-1 s 1\p DE-604 Mathematics and Its Applications 386 (DE-604)BV008163334 386 https://doi.org/10.1007/978-94-011-5426-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bandyopadhyay, Pratul Geometry, Topology and Quantization Mathematics and Its Applications Physics Global differential geometry Quantum theory Nuclear physics Theoretical, Mathematical and Computational Physics Quantum Physics Elementary Particles, Quantum Field Theory Nuclear Physics, Heavy Ions, Hadrons Differential Geometry Quantentheorie Geometrische Quantisierung (DE-588)4156720-1 gnd |
| subject_GND | (DE-588)4156720-1 |
| title | Geometry, Topology and Quantization |
| title_auth | Geometry, Topology and Quantization |
| title_exact_search | Geometry, Topology and Quantization |
| title_full | Geometry, Topology and Quantization by Pratul Bandyopadhyay |
| title_fullStr | Geometry, Topology and Quantization by Pratul Bandyopadhyay |
| title_full_unstemmed | Geometry, Topology and Quantization by Pratul Bandyopadhyay |
| title_short | Geometry, Topology and Quantization |
| title_sort | geometry topology and quantization |
| topic | Physics Global differential geometry Quantum theory Nuclear physics Theoretical, Mathematical and Computational Physics Quantum Physics Elementary Particles, Quantum Field Theory Nuclear Physics, Heavy Ions, Hadrons Differential Geometry Quantentheorie Geometrische Quantisierung (DE-588)4156720-1 gnd |
| topic_facet | Physics Global differential geometry Quantum theory Nuclear physics Theoretical, Mathematical and Computational Physics Quantum Physics Elementary Particles, Quantum Field Theory Nuclear Physics, Heavy Ions, Hadrons Differential Geometry Quantentheorie Geometrische Quantisierung |
| url | https://doi.org/10.1007/978-94-011-5426-0 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT bandyopadhyaypratul geometrytopologyandquantization |