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The covariant Stone–von Neumann theorem for locally compact quantum groups
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-12-19 DOI: 10.1007/s11005-024-01886-w
Lucas Hall, Leonard Huang, Jacek Krajczok, Mariusz Tobolski
{"title":"The covariant Stone–von Neumann theorem for locally compact quantum groups","authors":"Lucas Hall,&nbsp;Leonard Huang,&nbsp;Jacek Krajczok,&nbsp;Mariusz Tobolski","doi":"10.1007/s11005-024-01886-w","DOIUrl":"10.1007/s11005-024-01886-w","url":null,"abstract":"<div><p>The Stone–von Neumann theorem is a fundamental result which unified the competing quantum-mechanical models of matrix mechanics and wave mechanics. In this article, we continue the broad generalization set out by Huang and Ismert and by Hall, Huang, and Quigg, analyzing representations of locally compact quantum-dynamical systems defined on Hilbert modules, of which the classical result is a special case. We introduce a pair of modular representations which subsume numerous models available in the literature and, using the classical strategy of Rieffel, prove a Stone–von Neumann-type theorem for maximal actions of regular locally compact quantum groups on elementary C*-algebras. In particular, we generalize the Mackey–Stone–von Neumann theorem to regular locally compact quantum groups whose trivial actions on <span>(mathbb {C})</span> are maximal and recover the multiplicity results of Hall, Huang, and Quigg. With this characterization in hand, we prove our main result showing that if a dynamical system <span>((mathbb {G},A,alpha ))</span> satisfies the multiplicity assumption of the generalized Stone–von Neumann theorem, and if the coefficient algebra <i>A</i> admits a faithful state, then the spectrum of the iterated crossed product <span>(widehat{mathbb {G}}^textrm{op}ltimes (mathbb {G}ltimes A))</span> consists of a single point. In the case of a separable coefficient algebra or a regular acting quantum group, we further characterize features of this system, and thus obtain a partial converse to the Stone–von Neumann theorem in the quantum group setting. As a corollary, we show that a regular locally compact quantum group satisfies the generalized Stone–von Neumann theorem if and only if it is strongly regular.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the effect of derivative interactions in quantum field theory
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-12-19 DOI: 10.1007/s11005-024-01889-7
Karl-Henning Rehren
{"title":"On the effect of derivative interactions in quantum field theory","authors":"Karl-Henning Rehren","doi":"10.1007/s11005-024-01889-7","DOIUrl":"10.1007/s11005-024-01889-7","url":null,"abstract":"<div><p>There exist several good reasons why one may wish to add a total derivative to an interaction in quantum field theory, e.g., in order to improve the perturbative construction. Unlike in classical field theory, adding derivatives in general changes the theory. The analysis whether and how this can be prevented is presently limited to perturbative orders <span>(g^n)</span>, <span>(nle 3)</span>. We drastically simplify it by an all-orders formula, which also allows to answer some salient structural questions. The method is part of a larger program to (re)derive interactions of particles by quantum consistency conditions, rather than a classical principle of gauge invariance.\u0000\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01889-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lax structure and tau function for large BKP hierarchy 大型 BKP 层次结构的松弛结构和 tau 函数
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-12-16 DOI: 10.1007/s11005-024-01888-8
Wenchuang Guan, Shen Wang, Wenjuan Rui, Jipeng Cheng
{"title":"Lax structure and tau function for large BKP hierarchy","authors":"Wenchuang Guan,&nbsp;Shen Wang,&nbsp;Wenjuan Rui,&nbsp;Jipeng Cheng","doi":"10.1007/s11005-024-01888-8","DOIUrl":"10.1007/s11005-024-01888-8","url":null,"abstract":"<div><p>In this paper, we mainly investigate Lax structure and tau function for the large BKP hierarchy, which is also known as Toda hierarchy of B type. Firstly, the large BKP hierarchy can be derived from fermionic BKP hierarchy by using a special bosonization, which is presented in the form of bilinear equation. Then from bilinear equation, the corresponding Lax equation is given, where in particular the relation of flow generator with Lax operator is obtained. Also starting from Lax equation, the corresponding bilinear equation and existence of tau function are discussed. After that, large BKP hierarchy is viewed as sub-hierarchy of modified Toda (mToda) hierarchy, also called two-component first modified KP hierarchy. Finally by using two basic Miura transformations from mToda to Toda, we understand two typical relations between large BKP tau function <span>(tau _n(textbf{t}))</span> and Toda tau function <span>(tau _n^textrm{Toda}(textbf{t},-textbf{t}))</span>, that is, <span>(tau _n^{textrm{Toda}}(textbf{t},-{textbf{t}})=tau _n(textbf{t})tau _{n-1}(textbf{t}))</span> and <span>(tau _n^{textrm{Toda}}(textbf{t},-{textbf{t}})=tau _n^2(textbf{t}))</span>. Further, we find <span>(big (tau _n(textbf{t})tau _{n-1}(textbf{t}),tau _n^2(textbf{t})big ))</span> satisfies bilinear equation of mToda hierarchy.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Marginally outer trapped tubes in de Sitter spacetime 德西特时空中的边缘外困管
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-12-13 DOI: 10.1007/s11005-024-01884-y
Marc Mars, Carl Rossdeutscher, Walter Simon, Roland Steinbauer
{"title":"Marginally outer trapped tubes in de Sitter spacetime","authors":"Marc Mars,&nbsp;Carl Rossdeutscher,&nbsp;Walter Simon,&nbsp;Roland Steinbauer","doi":"10.1007/s11005-024-01884-y","DOIUrl":"10.1007/s11005-024-01884-y","url":null,"abstract":"<div><p>We prove two results which are relevant for constructing marginally outer trapped tubes (MOTTs) in de Sitter spacetime. The first one (Theorem 1) holds more generally, namely for spacetimes satisfying the null convergence condition and containing a timelike conformal Killing vector with a “temporal function”. We show that all marginally outer trapped surfaces (MOTSs) in such a spacetime are unstable. This prevents application of standard results on the propagation of stable MOTSs to MOTTs. On the other hand, it was shown recently, Charlton et al. (minimal surfaces and alternating multiple zetas, arXiv:2407.07130), that for every sufficiently high genus, there exists a smooth, complete family of CMC surfaces embedded in the round 3-sphere <span>(mathbb {S}^3)</span>. This family connects a Lawson minimal surface with a doubly covered geodesic 2-sphere. We show (Theorem 2) by a simple scaling argument that this result translates to an existence proof for complete MOTTs with CMC sections in de Sitter spacetime. Moreover, the area of these sections increases strictly monotonically. We compare this result with an area law obtained before for holographic screens.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01884-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142821466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Universal enveloping algebras of Lie–Rinehart algebras: crossed products, connections, and curvature
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-12-12 DOI: 10.1007/s11005-024-01876-y
Xavier Bekaert, Niels Kowalzig, Paolo Saracco
{"title":"Universal enveloping algebras of Lie–Rinehart algebras: crossed products, connections, and curvature","authors":"Xavier Bekaert,&nbsp;Niels Kowalzig,&nbsp;Paolo Saracco","doi":"10.1007/s11005-024-01876-y","DOIUrl":"10.1007/s11005-024-01876-y","url":null,"abstract":"<div><p>We extend a theorem, originally formulated by Blattner–Cohen–Montgomery for crossed products arising from Hopf algebras weakly acting on noncommutative algebras, to the realm of left Hopf algebroids. Our main motivation is an application to universal enveloping algebras of projective Lie–Rinehart algebras: for any given curved (resp. flat) connection, that is, a linear (resp. Lie–Rinehart) splitting of a Lie–Rinehart algebra extension, we provide a crossed (resp. smash) product decomposition of the associated universal enveloping algebra, and vice versa. As a geometric example, we describe the associative algebra generated by the invariant vector fields on the total space of a principal bundle as a crossed product of the algebra generated by the vertical ones and the algebra of differential operators on the base.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142811057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Appell–Lerch sums and (mathcal {N}=2) moduli
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-12-10 DOI: 10.1007/s11005-024-01887-9
Emile Bouaziz
{"title":"Appell–Lerch sums and (mathcal {N}=2) moduli","authors":"Emile Bouaziz","doi":"10.1007/s11005-024-01887-9","DOIUrl":"10.1007/s11005-024-01887-9","url":null,"abstract":"<div><p>We study moduli of suitably framed <span>(mathcal {N}=2)</span> elliptic curves. We introduce the notion of <i>tameness</i> for a family of super-spaces and show that the non-tameness of the resulting universal family is essentially controlled by the Appell–Lerch sum <span>(kappa )</span>, familiar from the theory of mock modular forms. In this optic, <span>(kappa )</span> arises when considering purely Fermionic deformations of <span>(mathcal {N}=2)</span> elliptic curves.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142798288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Sine–Gordon QFT in de Sitter spacetime 德西特时空中的辛-戈登 QFT
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-28 DOI: 10.1007/s11005-024-01882-0
Daniela Cadamuro, Markus B. Fröb, Carolina Moreira Ferrera
{"title":"The Sine–Gordon QFT in de Sitter spacetime","authors":"Daniela Cadamuro,&nbsp;Markus B. Fröb,&nbsp;Carolina Moreira Ferrera","doi":"10.1007/s11005-024-01882-0","DOIUrl":"10.1007/s11005-024-01882-0","url":null,"abstract":"<div><p>We consider the massless Sine–Gordon model in de Sitter spacetime, in the regime <span>(beta ^2 &lt; 4 pi )</span> and using the framework of perturbative algebraic quantum field theory. We show that a Fock space representation exists for the free massless field, but that the natural one-parameter family of vacuum-like states breaks the de Sitter boost symmetries. We prove convergence of the perturbative series for the S matrix in this representation and construct the interacting Haag–Kastler net of local algebras from the relative S matrices. We show that the net fulfills isotony, locality and de Sitter covariance (in the algebraic adiabatic limit), even though the states that we consider are not invariant. We furthermore prove convergence of the perturbative series for the interacting field and the vertex operators, and verify that the interacting equation of motion holds.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01882-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142736902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ruijsenaars wavefunctions as modular group matrix coefficients 作为模块组矩阵系数的鲁伊塞纳斯波函数
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-27 DOI: 10.1007/s11005-024-01881-1
Philippe Di Francesco, Rinat Kedem, Sergey Khoroshkin, Gus Schrader, Alexander Shapiro
{"title":"Ruijsenaars wavefunctions as modular group matrix coefficients","authors":"Philippe Di Francesco,&nbsp;Rinat Kedem,&nbsp;Sergey Khoroshkin,&nbsp;Gus Schrader,&nbsp;Alexander Shapiro","doi":"10.1007/s11005-024-01881-1","DOIUrl":"10.1007/s11005-024-01881-1","url":null,"abstract":"<div><p>We give a description of the Hallnäs–Ruijsenaars eigenfunctions of the 2-particle hyperbolic Ruijsenaars system as matrix coefficients for the order 4 element <span>(Sin SL(2,{mathbb {Z}}))</span> acting on the Hilbert space of <i>GL</i>(2) quantum Teichmüller theory on the punctured torus. The <i>GL</i>(2) Macdonald polynomials are then obtained as special values of the analytic continuation of these matrix coefficients. The main tool used in the proof is the cluster structure on the moduli space of framed <i>GL</i>(2)-local systems on the punctured torus, and an <span>(SL(2,{mathbb {Z}}))</span>-equivariant embedding of the <i>GL</i>(2) spherical DAHA into the quantized coordinate ring of the corresponding cluster Poisson variety.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01881-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142736935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-time measurement of entropy transfer in Markovian quantum dynamics 马尔可夫量子动力学中熵转移的两次测量
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-27 DOI: 10.1007/s11005-024-01880-2
Alain Joye, Claude-Alain Pillet
{"title":"Two-time measurement of entropy transfer in Markovian quantum dynamics","authors":"Alain Joye,&nbsp;Claude-Alain Pillet","doi":"10.1007/s11005-024-01880-2","DOIUrl":"10.1007/s11005-024-01880-2","url":null,"abstract":"<div><p>We consider a protocol for the two-time measurement of entropic observables in quantum open systems driven out of thermal equilibrium by coupling to several heat baths. We concentrate on the Markovian approximation of the time-evolution and relate the expected value of the so defined entropy variations with the well-known expression of entropy production due to Lebowitz and Spohn. We do so under the detailed balance condition and, as a byproduct, we show that the probabilities of outcomes of two-time measurements are given by a continuous time Markov process determined by the Lindblad generator of the Markovian quantum dynamics.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142736936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Boolean TQFTs with accumulating defects, sofic systems, and automata for infinite words 具有累积缺陷的布尔 TQFT、sofic 系统和无限词的自动机
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1007/s11005-024-01885-x
Paul Gustafson, Mee Seong Im, Mikhail Khovanov
{"title":"Boolean TQFTs with accumulating defects, sofic systems, and automata for infinite words","authors":"Paul Gustafson,&nbsp;Mee Seong Im,&nbsp;Mikhail Khovanov","doi":"10.1007/s11005-024-01885-x","DOIUrl":"10.1007/s11005-024-01885-x","url":null,"abstract":"<div><p>Any finite state automaton gives rise to a Boolean one-dimensional TQFT with defects and inner endpoints of cobordisms. This paper extends the correspondence to Boolean TQFTs where defects accumulate towards inner endpoints, relating such TQFTs and topological theories to sofic systems and <span>(omega )</span>-automata.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","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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