Noncommutative mathematics for quantum systems /:
"Discusses two current areas of noncommutative mathematics, quantum probability and quantum dynamical systems"--
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Cambridge University Press,
[2016]
|
| Schriftenreihe: | Cambridge - IISc series.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "Discusses two current areas of noncommutative mathematics, quantum probability and quantum dynamical systems"-- |
| Beschreibung: | Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physics and operator algebras. |
| Beschreibung: | 1 online resource (xviii, 180 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781316562857 1316562859 9781316675304 1316675300 |
Internformat
MARC
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| 245 | 1 | 0 | |a Noncommutative mathematics for quantum systems / |c Uwe Franz, Adam Skalski. |
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| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a "Discusses two current areas of noncommutative mathematics, quantum probability and quantum dynamical systems"-- |c Provided by publisher | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Title; Copyright; Dedication; Contents; Preface; Conference photo; Introduction; 1 Independence and Lévy Processes in Quantum Probability; 1.1 Introduction; 1.2 What is Quantum Probability?; 1.2.1 Distinguishing features of classical and quantum probability; 1.2.2 Dictionary 'Classical ₄!Quantum'; 1.3 Why do we Need Quantum Probability?; 1.3.1 Mermin's version of the EPR experiment; 1.3.2 Gleason's theorem; 1.3.3 The Kochen-Specker theorem; 1.4 Infinite Divisibility in Classical Probability; 1.4.1 Stochastic independence; 1.4.2 Convolution. | |
| 500 | |a Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physics and operator algebras. | ||
| 505 | 8 | |a 1.4.3 Infinite divisibility, continuous convolution semigroups, and Lévy processes1.4.4 The De Finetti-Lévy-Khintchine formula on (R+, +); 1.4.5 Lévy-Khintchine formulae on cones; 1.4.6 The Lévy-Khintchine formula on (Rd, +); 1.4.7 The Markov semigroup of a Lévy process; 1.4.8 Hunt's formula; 1.5 Lévy Processes on Involutive Bialgebras. | |
| 505 | 8 | |a 1.5.1 Definition of Lévy processes on involutive bialgebras 1.5.2 The generating functional of a Lévy process ; 1.5.3 The Schürmann triple of a Lévy process; 1.5.4 Examples. | |
| 505 | 8 | |a 1.6 Lévy Processes on Compact Quantum Groups and their Markov Semigroups 1.6.1 Compact quantum groups; 1.6.2 Translation invariant Markov semigroups; 1.7 Independences and Convolutions in Noncommutative Probability; 1.7.1 Nevanlinna theory and Cauchy-Stieltjes transforms; 1.7.2 Free convolutions; 1.7.3 A useful Lemma; 1.7.4 Monotone convolutions. | |
| 505 | 8 | |a 1.7.5 Boolean convolutions1.8 The Five Universal Independences; 1.8.1 Algebraic probability spaces; 1.8.2 Classical stochastic independence and the product of probability spaces; 1.8.3 Products of algebraic probability spaces; 1.8.4 Classification of the universal independences; 1.9 Lévy Processes on Dual Groups ; 1.9.1 Dual groups. | |
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| 650 | 6 | |a Probabilités. | |
| 650 | 6 | |a Théorie quantique. | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn934451642 |
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| adam_text | |
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| author | Franz, Uwe Skalski, Adam, 1978- |
| author_GND | http://id.loc.gov/authorities/names/n99047150 http://id.loc.gov/authorities/names/n2015052235 |
| author_facet | Franz, Uwe Skalski, Adam, 1978- |
| author_role | aut aut |
| author_sort | Franz, Uwe |
| author_variant | u f uf a s as |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.17.P68 F73 2016eb |
| callnumber-search | QC174.17.P68 F73 2016eb |
| callnumber-sort | QC 3174.17 P68 F73 42016EB |
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| contents | Cover; Title; Copyright; Dedication; Contents; Preface; Conference photo; Introduction; 1 Independence and Lévy Processes in Quantum Probability; 1.1 Introduction; 1.2 What is Quantum Probability?; 1.2.1 Distinguishing features of classical and quantum probability; 1.2.2 Dictionary 'Classical ₄!Quantum'; 1.3 Why do we Need Quantum Probability?; 1.3.1 Mermin's version of the EPR experiment; 1.3.2 Gleason's theorem; 1.3.3 The Kochen-Specker theorem; 1.4 Infinite Divisibility in Classical Probability; 1.4.1 Stochastic independence; 1.4.2 Convolution. 1.4.3 Infinite divisibility, continuous convolution semigroups, and Lévy processes1.4.4 The De Finetti-Lévy-Khintchine formula on (R+, +); 1.4.5 Lévy-Khintchine formulae on cones; 1.4.6 The Lévy-Khintchine formula on (Rd, +); 1.4.7 The Markov semigroup of a Lévy process; 1.4.8 Hunt's formula; 1.5 Lévy Processes on Involutive Bialgebras. 1.5.1 Definition of Lévy processes on involutive bialgebras 1.5.2 The generating functional of a Lévy process ; 1.5.3 The Schürmann triple of a Lévy process; 1.5.4 Examples. 1.6 Lévy Processes on Compact Quantum Groups and their Markov Semigroups 1.6.1 Compact quantum groups; 1.6.2 Translation invariant Markov semigroups; 1.7 Independences and Convolutions in Noncommutative Probability; 1.7.1 Nevanlinna theory and Cauchy-Stieltjes transforms; 1.7.2 Free convolutions; 1.7.3 A useful Lemma; 1.7.4 Monotone convolutions. 1.7.5 Boolean convolutions1.8 The Five Universal Independences; 1.8.1 Algebraic probability spaces; 1.8.2 Classical stochastic independence and the product of probability spaces; 1.8.3 Products of algebraic probability spaces; 1.8.4 Classification of the universal independences; 1.9 Lévy Processes on Dual Groups ; 1.9.1 Dual groups. |
| ctrlnum | (OCoLC)934451642 |
| dewey-full | 530.13/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13/3 |
| dewey-search | 530.13/3 |
| dewey-sort | 3530.13 13 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| genre | Electronic books. |
| genre_facet | Electronic books. |
| id | ZDB-4-EBA-ocn934451642 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:26:59Z |
| institution | BVB |
| isbn | 9781316562857 1316562859 9781316675304 1316675300 |
| language | English |
| oclc_num | 934451642 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xviii, 180 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Cambridge - IISc series. |
| series2 | Cambridge - IISc series |
| spelling | Franz, Uwe, author. http://id.loc.gov/authorities/names/n99047150 Noncommutative mathematics for quantum systems / Uwe Franz, Adam Skalski. New York : Cambridge University Press, [2016] 1 online resource (xviii, 180 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge - IISc series Includes bibliographical references and index. "Discusses two current areas of noncommutative mathematics, quantum probability and quantum dynamical systems"-- Provided by publisher Print version record. Cover; Title; Copyright; Dedication; Contents; Preface; Conference photo; Introduction; 1 Independence and Lévy Processes in Quantum Probability; 1.1 Introduction; 1.2 What is Quantum Probability?; 1.2.1 Distinguishing features of classical and quantum probability; 1.2.2 Dictionary 'Classical ₄!Quantum'; 1.3 Why do we Need Quantum Probability?; 1.3.1 Mermin's version of the EPR experiment; 1.3.2 Gleason's theorem; 1.3.3 The Kochen-Specker theorem; 1.4 Infinite Divisibility in Classical Probability; 1.4.1 Stochastic independence; 1.4.2 Convolution. Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physics and operator algebras. 1.4.3 Infinite divisibility, continuous convolution semigroups, and Lévy processes1.4.4 The De Finetti-Lévy-Khintchine formula on (R+, +); 1.4.5 Lévy-Khintchine formulae on cones; 1.4.6 The Lévy-Khintchine formula on (Rd, +); 1.4.7 The Markov semigroup of a Lévy process; 1.4.8 Hunt's formula; 1.5 Lévy Processes on Involutive Bialgebras. 1.5.1 Definition of Lévy processes on involutive bialgebras 1.5.2 The generating functional of a Lévy process ; 1.5.3 The Schürmann triple of a Lévy process; 1.5.4 Examples. 1.6 Lévy Processes on Compact Quantum Groups and their Markov Semigroups 1.6.1 Compact quantum groups; 1.6.2 Translation invariant Markov semigroups; 1.7 Independences and Convolutions in Noncommutative Probability; 1.7.1 Nevanlinna theory and Cauchy-Stieltjes transforms; 1.7.2 Free convolutions; 1.7.3 A useful Lemma; 1.7.4 Monotone convolutions. 1.7.5 Boolean convolutions1.8 The Five Universal Independences; 1.8.1 Algebraic probability spaces; 1.8.2 Classical stochastic independence and the product of probability spaces; 1.8.3 Products of algebraic probability spaces; 1.8.4 Classification of the universal independences; 1.9 Lévy Processes on Dual Groups ; 1.9.1 Dual groups. Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Potential theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85105671 Probability https://id.nlm.nih.gov/mesh/D011336 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Probabilités. Théorie quantique. Théorie du potentiel. probability. aat SCIENCE Energy. bisacsh SCIENCE Mechanics General. bisacsh SCIENCE Physics General. bisacsh Probabilidades embne Potencial, Teoría del (Matemáticas) embucm Potential theory (Mathematics) fast Probabilities fast Quantum theory fast Electronic books. Skalski, Adam, 1978- author. https://id.oclc.org/worldcat/entity/E39PBJtGXHtc6H3jc7K68whJXd http://id.loc.gov/authorities/names/n2015052235 has work: Noncommutative mathematics for quantum systems (Text) https://id.oclc.org/worldcat/entity/E39PCFJJ6Tw9kyBrpXxQddprjd https://id.oclc.org/worldcat/ontology/hasWork Print version: Franz, Uwe. Noncommutative mathematics for quantum systems 9781107148055 (DLC) 2015032903 (OCoLC)919316281 Cambridge - IISc series. http://id.loc.gov/authorities/names/no2016067031 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1159408 Volltext |
| spellingShingle | Franz, Uwe Skalski, Adam, 1978- Noncommutative mathematics for quantum systems / Cambridge - IISc series. Cover; Title; Copyright; Dedication; Contents; Preface; Conference photo; Introduction; 1 Independence and Lévy Processes in Quantum Probability; 1.1 Introduction; 1.2 What is Quantum Probability?; 1.2.1 Distinguishing features of classical and quantum probability; 1.2.2 Dictionary 'Classical ₄!Quantum'; 1.3 Why do we Need Quantum Probability?; 1.3.1 Mermin's version of the EPR experiment; 1.3.2 Gleason's theorem; 1.3.3 The Kochen-Specker theorem; 1.4 Infinite Divisibility in Classical Probability; 1.4.1 Stochastic independence; 1.4.2 Convolution. 1.4.3 Infinite divisibility, continuous convolution semigroups, and Lévy processes1.4.4 The De Finetti-Lévy-Khintchine formula on (R+, +); 1.4.5 Lévy-Khintchine formulae on cones; 1.4.6 The Lévy-Khintchine formula on (Rd, +); 1.4.7 The Markov semigroup of a Lévy process; 1.4.8 Hunt's formula; 1.5 Lévy Processes on Involutive Bialgebras. 1.5.1 Definition of Lévy processes on involutive bialgebras 1.5.2 The generating functional of a Lévy process ; 1.5.3 The Schürmann triple of a Lévy process; 1.5.4 Examples. 1.6 Lévy Processes on Compact Quantum Groups and their Markov Semigroups 1.6.1 Compact quantum groups; 1.6.2 Translation invariant Markov semigroups; 1.7 Independences and Convolutions in Noncommutative Probability; 1.7.1 Nevanlinna theory and Cauchy-Stieltjes transforms; 1.7.2 Free convolutions; 1.7.3 A useful Lemma; 1.7.4 Monotone convolutions. 1.7.5 Boolean convolutions1.8 The Five Universal Independences; 1.8.1 Algebraic probability spaces; 1.8.2 Classical stochastic independence and the product of probability spaces; 1.8.3 Products of algebraic probability spaces; 1.8.4 Classification of the universal independences; 1.9 Lévy Processes on Dual Groups ; 1.9.1 Dual groups. Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Potential theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85105671 Probability https://id.nlm.nih.gov/mesh/D011336 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Probabilités. Théorie quantique. Théorie du potentiel. probability. aat SCIENCE Energy. bisacsh SCIENCE Mechanics General. bisacsh SCIENCE Physics General. bisacsh Probabilidades embne Potencial, Teoría del (Matemáticas) embucm Potential theory (Mathematics) fast Probabilities fast Quantum theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85107090 http://id.loc.gov/authorities/subjects/sh85109469 http://id.loc.gov/authorities/subjects/sh85105671 https://id.nlm.nih.gov/mesh/D011336 https://id.nlm.nih.gov/mesh/D011789 |
| title | Noncommutative mathematics for quantum systems / |
| title_auth | Noncommutative mathematics for quantum systems / |
| title_exact_search | Noncommutative mathematics for quantum systems / |
| title_full | Noncommutative mathematics for quantum systems / Uwe Franz, Adam Skalski. |
| title_fullStr | Noncommutative mathematics for quantum systems / Uwe Franz, Adam Skalski. |
| title_full_unstemmed | Noncommutative mathematics for quantum systems / Uwe Franz, Adam Skalski. |
| title_short | Noncommutative mathematics for quantum systems / |
| title_sort | noncommutative mathematics for quantum systems |
| topic | Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Potential theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85105671 Probability https://id.nlm.nih.gov/mesh/D011336 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Probabilités. Théorie quantique. Théorie du potentiel. probability. aat SCIENCE Energy. bisacsh SCIENCE Mechanics General. bisacsh SCIENCE Physics General. bisacsh Probabilidades embne Potencial, Teoría del (Matemáticas) embucm Potential theory (Mathematics) fast Probabilities fast Quantum theory fast |
| topic_facet | Probabilities. Quantum theory. Potential theory (Mathematics) Probability Quantum Theory Probabilités. Théorie quantique. Théorie du potentiel. probability. SCIENCE Energy. SCIENCE Mechanics General. SCIENCE Physics General. Probabilidades Potencial, Teoría del (Matemáticas) Probabilities Quantum theory Electronic books. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1159408 |
| work_keys_str_mv | AT franzuwe noncommutativemathematicsforquantumsystems AT skalskiadam noncommutativemathematicsforquantumsystems |