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Infinite Dimensional Analysis Quantum Probability and Related Topics最新文献

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COVARIANT QUANTUM FIELDS VIA LORENTZ GROUP REPRESENTATION OF WEYL OPERATORS 通过weyl算子的洛伦兹群表示的协变量子场
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0002
Radhakrishnan Balu
{"title":"COVARIANT QUANTUM FIELDS VIA LORENTZ GROUP REPRESENTATION OF WEYL OPERATORS","authors":"Radhakrishnan Balu","doi":"10.1142/9789811275999_0002","DOIUrl":"https://doi.org/10.1142/9789811275999_0002","url":null,"abstract":"The building blocks of Hudson-Parthasarathy quantum stochastic calculus start with Weyl operators on a symmetric Fock space. To realize a relativistically covariant version of the calculus we construct representations of Poincare group in terms of Weyl operators on suitably constructed, Bosonic or Fermionic based on the mass and spin of the fundamental particle, Fock spaces. We proceed by describing the orbits of homogeneous Lorentz group on R4 and build fiber bundle representations of Poincare group induced from the stabilizer subgroups (little groups) and build the Boson Fock space of the Hilbert space formed from the sections of the bundle. Our Weyl operators are constructed on symmetric Fock space of this space and the corresponding annihilation, creation, and conservation operators are synthesized in the usual fashion in relativistic theories for space-like, time-like, and light-like fields. We achieve this by constructing transitive systems of imprimitivity (second-quantized SI), which are dynamical systems with trajectories dense in the configuration space, by induced representations. We provide the details of the field operators for the case of massive Bosons as the rest are similar in construction and indicate the ways to construct adapted processes paving way for building covariant quantum stochastic calculus.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136018461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
BI-MONOTONE BROWNIAN MOTION 双单调布朗运动
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0005
Malte Gerhold
{"title":"BI-MONOTONE BROWNIAN MOTION","authors":"Malte Gerhold","doi":"10.1142/9789811275999_0005","DOIUrl":"https://doi.org/10.1142/9789811275999_0005","url":null,"abstract":"We define bi-monotone independence, prove a bi-monotone central limit theorem and use it to study the distribution of bi-monotone Brownian motion, which is defined as the two-dimensional operator process with monotone and antimonotone Brownian motion as components.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136017530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
ON EFFECTIVE METHODS OF INVESTIGATION OF NONPOSITIVE MAPS 论非正图调查的有效方法
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0009
ANDRZEJ JAMIOŁKOWSKI
{"title":"ON EFFECTIVE METHODS OF INVESTIGATION OF NONPOSITIVE MAPS","authors":"ANDRZEJ JAMIOŁKOWSKI","doi":"10.1142/9789811275999_0009","DOIUrl":"https://doi.org/10.1142/9789811275999_0009","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A COMBINED QUANTUM ALGORITHM AND ITS COMPUTATIONAL COMPLEXITY 一种组合量子算法及其计算复杂度
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0008
SATOSHI IRIYAMA
{"title":"A COMBINED QUANTUM ALGORITHM AND ITS COMPUTATIONAL COMPLEXITY","authors":"SATOSHI IRIYAMA","doi":"10.1142/9789811275999_0008","DOIUrl":"https://doi.org/10.1142/9789811275999_0008","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
REPRESENTING THE QUANTUM OPERATORS IN TERMS OF MULTIPLICATION AND DIFFERENTIATION OPERATORS 用乘法和微分算子表示量子算子
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0018
GABRIELA POPA, AUREL I. STAN
{"title":"REPRESENTING THE QUANTUM OPERATORS IN TERMS OF MULTIPLICATION AND DIFFERENTIATION OPERATORS","authors":"GABRIELA POPA, AUREL I. STAN","doi":"10.1142/9789811275999_0018","DOIUrl":"https://doi.org/10.1142/9789811275999_0018","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
CONDITIONAL DISTRIBUTION OF A RANDOM VARIABLE, CONDITIONED BY HIDA DISTRIBUTIONS, ON EUCLIDEAN QUANTUM FIELDS 欧几里得量子场上随机变量的条件分布，由hida分布决定
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0021
M. W. YOSHIDA
{"title":"CONDITIONAL DISTRIBUTION OF A RANDOM VARIABLE, CONDITIONED BY HIDA DISTRIBUTIONS, ON EUCLIDEAN QUANTUM FIELDS","authors":"M. W. YOSHIDA","doi":"10.1142/9789811275999_0021","DOIUrl":"https://doi.org/10.1142/9789811275999_0021","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ROUGH-PATHS AND NON-COMMUTATIVE PROBABILITY 粗糙路径和非交换概率
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0016
REN SCHOTT
{"title":"ROUGH-PATHS AND NON-COMMUTATIVE PROBABILITY","authors":"REN SCHOTT","doi":"10.1142/9789811275999_0016","DOIUrl":"https://doi.org/10.1142/9789811275999_0016","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ENTANGLEMENT AND ITS CONDITIONALITY 纠缠及其条件
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0011
TAKASHI MATSUOKA
{"title":"ENTANGLEMENT AND ITS CONDITIONALITY","authors":"TAKASHI MATSUOKA","doi":"10.1142/9789811275999_0011","DOIUrl":"https://doi.org/10.1142/9789811275999_0011","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
QUANTUM-LIKE MODELING OF THE ORDER EFFECT IN DECISION MAKING: POVM VIEWPOINT ON THE WANG-BUSEMEYER QQ-EQUALITY 决策中顺序效应的量子建模:关于wang-busemeyer q -等式的povm观点
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0010
Aleksandr Lebedev, Andrei Khrennikov
{"title":"QUANTUM-LIKE MODELING OF THE ORDER EFFECT IN DECISION MAKING: POVM VIEWPOINT ON THE WANG-BUSEMEYER QQ-EQUALITY","authors":"Aleksandr Lebedev, Andrei Khrennikov","doi":"10.1142/9789811275999_0010","DOIUrl":"https://doi.org/10.1142/9789811275999_0010","url":null,"abstract":"In recent years, quantum mechanics has been actively used in areas outside of physics, such as psychology, sociology, theory of decision-making, game theory, and others. In particular, quantum mechanics is used to explain the paradoxes arising in cognitive psychology and decision making. Wang and Busemeyer invented a quantum model and approach as well as non-parametric equality (so-called QQ-equality), explaining the questions order effect. The primary objective of this note is to test the possibility to expand the Wang-Busemeyer model by considering questions which are mathematically represented by positive operator valued measures. We found that, for such observables, the QQ-equality can be violated. But, we also showed that, in principle, it is possible to reduce expanded model to the original Wang-Busemeyer model by expanding the context of the questions.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136102262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
LÉVY PROCESSES ON THE LORENTZ-LIE ALGEBRA LÉvy洛伦兹-李代数的过程
4区 数学
Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI: 10.1142/9789811275999_0003
Ameur Dhahri, Uwe Franz
{"title":"LÉVY PROCESSES ON THE LORENTZ-LIE ALGEBRA","authors":"Ameur Dhahri, Uwe Franz","doi":"10.1142/9789811275999_0003","DOIUrl":"https://doi.org/10.1142/9789811275999_0003","url":null,"abstract":"Levy processes in the sense of Schurmann on the Lie algebra of the Lorentz grouop are studied. It is known that only one of the irreducible unitary representations of the Lorentz group admits a non-trivial one-cocycle. A Schurmann triple is constructed for this cocycle and the properties of the associated Levy process are investigated. The decommpositions of the restrictions of this triple to the Lie subalgebras $so(3)$ and $so(2,1)$ are described.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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