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A SymTFT for Continuous Symmetries 连续对称的 SymTFT
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-11 DOI: arxiv-2401.06128
T. Daniel Brennan, Zhengdi Sun
{"title":"A SymTFT for Continuous Symmetries","authors":"T. Daniel Brennan, Zhengdi Sun","doi":"arxiv-2401.06128","DOIUrl":"https://doi.org/arxiv-2401.06128","url":null,"abstract":"Symmetry is a powerful tool for studying dynamics in QFT as they provide\u0000selection rules, constrain RG flows, and allow for simplified dynamics.\u0000Currently, our understanding is that the most general form of symmetry is\u0000described by categorical symmetries which can be realized via Symmetry TQFTs or\u0000``SymTFTs.\" In this paper, we show how the framework of the SymTFT, which is\u0000understood for discrete symmetries (i.e. finite categorical symmetries), can be\u0000generalized to continuous symmetries. In addition to demonstrating how $U(1)$\u0000global symmetries can be incorporated into the paradigm of the SymTFT, we apply\u0000our formalism to construct the SymTFT for the $mathbb{Q}/mathbb{Z}$\u0000non-invertible chiral symmetry in $4d$ theories, demonstrate how symmetry\u0000fractionalization is realized SymTFTs, and conjecture the SymTFT for general\u0000continuous $G^{(0)}$ global symmetries.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fate of $κ$-Minkowski space-time in non relativistic (Galilean) and ultra-relativistic (Carrollian) regimes 非相对论（伽利略）和超相对论（卡罗尔）状态下κ$-闵科夫斯基时空的命运
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-11 DOI: arxiv-2401.05769
Deeponjit Bose, Anwesha Chakraborty, Biswajit Chakraborty
{"title":"Fate of $κ$-Minkowski space-time in non relativistic (Galilean) and ultra-relativistic (Carrollian) regimes","authors":"Deeponjit Bose, Anwesha Chakraborty, Biswajit Chakraborty","doi":"arxiv-2401.05769","DOIUrl":"https://doi.org/arxiv-2401.05769","url":null,"abstract":"Here, we present an algebraic and kinematical analysis of non-commutative\u0000$kappa$-Minkowski spaces within Galilean (non-relativistic) and Carrollian\u0000(ultra-relativistic) regimes. Utilizing the theory of Wigner-In\"{o}nu\u0000contractions, we begin with a brief review of how one can apply these\u0000contractions to the well-known Poincar'{e} algebra, yielding the corresponding\u0000Galilean (both massive and mass-less) and Carrollian algebras as $c to infty$\u0000and $cto 0$, respectively. Subsequently, we methodically apply these\u0000contractions to non-commutative $kappa$-deformed spaces, revealing compelling\u0000insights into the interplay among the non-commutative parameters $a^mu$ (with\u0000$|a^nu|$ being of the order of Planck length scale) and the speed of light $c$\u0000as it approaches both infinity and zero. Our exploration predicts a sort of\u0000\"branching\" of the non-commutative parameters $a^mu$, leading to the emergence\u0000of a novel length scale and time scale in either limit. Furthermore, our\u0000investigation extends to the examination of curved momentum spaces and their\u0000geodesic distances in appropriate subspaces of the $kappa$-deformed Newtonian\u0000and Carrollian space-times. We finally delve into the study of their deformed\u0000dispersion relations, arising from these deformed geodesic distances, providing\u0000a comprehensive understanding of the nature of these space-times.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rado matroids and a graphical calculus for boundaries of Wilson loop diagrams 拉多矩阵和威尔逊环图边界的图形微积分
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-10 DOI: arxiv-2401.05592
Susama Agarwala, Colleen Delaney, Karen Yeats
{"title":"Rado matroids and a graphical calculus for boundaries of Wilson loop diagrams","authors":"Susama Agarwala, Colleen Delaney, Karen Yeats","doi":"arxiv-2401.05592","DOIUrl":"https://doi.org/arxiv-2401.05592","url":null,"abstract":"We study the boundaries of the positroid cells which arise from N = 4 super\u0000Yang Mills theory. Our main tool is a new diagrammatic object which generalizes\u0000the Wilson loop diagrams used to represent interactions in the theory. We prove\u0000conditions under which these new generalized Wilson loop diagrams correspond to\u0000positroids and give an explicit algorithm to calculate the Grassmann necklace\u0000of said positroids. Then we develop a graphical calculus operating directly on\u0000noncrossing generalized Wilson loop diagrams. In this paradigm, applying\u0000diagrammatic moves to a generalized Wilson loop diagram results in new diagrams\u0000that represent boundaries of its associated positroid, without passing through\u0000cryptomorphisms. We provide a Python implementation of the graphical calculus\u0000and use it to show that the boundaries of positroids associated to ordinary\u0000Wilson loop diagram are generated by our diagrammatic moves in certain cases.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The random field Ising chain domain-wall structure in the large interaction limit 大相互作用极限下的随机场伊辛链域壁结构
arXiv - PHYS - Mathematical Physics Pub Date : 2024-01-08 DOI: arxiv-2401.03927
Orphée Collin, Giambattista Giacomin, Yueyun Hu
{"title":"The random field Ising chain domain-wall structure in the large interaction limit","authors":"Orphée Collin, Giambattista Giacomin, Yueyun Hu","doi":"arxiv-2401.03927","DOIUrl":"https://doi.org/arxiv-2401.03927","url":null,"abstract":"We study the configurations of the nearest neighbor Ising ferromagnetic chain\u0000with IID centered and square integrable external random field in the limit in\u0000which the pairwise interaction tends to infinity. The available free energy\u0000estimates for this model show a strong form of disorder relevance, i.e., a\u0000strong effect of disorder on the free energy behavior, and our aim is to make\u0000explicit how the disorder affects the spin configurations. We give a\u0000quantitative estimate that shows that the infinite volume spin configurations\u0000are close to one explicit disorder dependent configuration when the interaction\u0000is large. Our results confirm the predictions on this model obtained in D. S.\u0000Fisher, P. Le Doussal and C. Monthus (Phys. Rev. E 2001) by applying the\u0000renormalization group method introduced by D. S. Fisher (Phys. Rev. B 1995).","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139409021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inferring the dynamics of ionic currents from recursive piecewise data assimilation of approximate neuron models 从近似神经元模型的递归分片数据同化中推断离子电流的动态变化
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-20 DOI: arxiv-2312.12888
Stephen A. Wells, Joseph D. Taylor, Paul G. Morris, Alain Nogaret
{"title":"Inferring the dynamics of ionic currents from recursive piecewise data assimilation of approximate neuron models","authors":"Stephen A. Wells, Joseph D. Taylor, Paul G. Morris, Alain Nogaret","doi":"arxiv-2312.12888","DOIUrl":"https://doi.org/arxiv-2312.12888","url":null,"abstract":"We construct neuron models from data by transferring information from an\u0000observed time series to the state variables and parameters of Hodgkin-Huxley\u0000models. When the learning period completes, the model will predict additional\u0000observations and its parameters uniquely characterise the complement of ion\u0000channels. However, the assimilation of biological data, as opposed to model\u0000data, is complicated by the lack of knowledge of the true neuron equations.\u0000Reliance on guessed conductance models is plagued with multi-valued parameter\u0000solutions. Here, we report on the distributions of parameters and currents\u0000predicted with intentionally erroneous models, over-specified models, and an\u0000approximate model fitting hippocampal neuron data. We introduce a recursive\u0000piecewise data assimilation (RPDA) algorithm that converges with near-perfect\u0000reliability when the model is known. When the model is unknown, we show model\u0000error introduces correlations between certain parameters. The ionic currents\u0000reconstructed from these parameters are excellent predictors of true currents\u0000and carry a higher degree of confidence, >95.5%, than underlying parameters,\u0000>53%. Unexpressed ionic currents are correctly filtered out even in the\u0000presence of mild model error. When the model is unknown, the covariance\u0000eigenvalues of parameter estimates are found to be a good gauge of model error.\u0000Our results suggest that biological information may be retrieved from data by\u0000focussing on current estimates rather than parameters.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138823473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Calogero-Moser-Sutherland systems 卡洛吉罗-莫瑟-萨瑟兰系统
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-20 DOI: arxiv-2312.12932
Martin Hallnäs
{"title":"Calogero-Moser-Sutherland systems","authors":"Martin Hallnäs","doi":"arxiv-2312.12932","DOIUrl":"https://doi.org/arxiv-2312.12932","url":null,"abstract":"We discuss integrable many-body systems in one dimension of\u0000Calogero-Moser-Sutherland type, both classical and quantum as well as\u0000nonrelativistic and relativistic. In particular, we consider fundamental\u0000properties such as integrability, the existence of explicit solutions as well\u0000as action-angle and bispectral dualities that relate different such systems. We\u0000also briefly discuss the early history of the subject and indicate connections\u0000with other integrable systems.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138823538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A naturally appearing family of Cantorvals 一个自然出现的康托伐尔族
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-15 DOI: arxiv-2401.05372
Michael BaakeBielefeld, Anton GorodetskiIrvine, Jan MazáčBielefeld
{"title":"A naturally appearing family of Cantorvals","authors":"Michael BaakeBielefeld, Anton GorodetskiIrvine, Jan MazáčBielefeld","doi":"arxiv-2401.05372","DOIUrl":"https://doi.org/arxiv-2401.05372","url":null,"abstract":"The aim of this note is to show the existence of a large family of Cantorvals\u0000arising in the projection description of primitive two-letter substitutions.\u0000This provides a new, naturally occurring class of Cantorvals.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constructor Theory as Process Theory 作为过程理论的构造理论
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-14 DOI: arxiv-2401.05364
Stefano GogiosoHashberg Ltd, Vincent Wang-MaścianicaQuantinuum Ltd, Muhammad Hamza WaseemQuantinuum Ltd, Carlo Maria ScandoloUniversity of Calgary, Bob CoeckeQuantinuum Ltd
{"title":"Constructor Theory as Process Theory","authors":"Stefano GogiosoHashberg Ltd, Vincent Wang-MaścianicaQuantinuum Ltd, Muhammad Hamza WaseemQuantinuum Ltd, Carlo Maria ScandoloUniversity of Calgary, Bob CoeckeQuantinuum Ltd","doi":"arxiv-2401.05364","DOIUrl":"https://doi.org/arxiv-2401.05364","url":null,"abstract":"Constructor theory is a meta-theoretic approach that seeks to characterise\u0000concrete theories of physics in terms of the (im)possibility to implement\u0000certain abstract \"tasks\" by means of physical processes. Process theory, on the\u0000other hand, pursues analogous characterisation goals in terms of the\u0000compositional structure of said processes, concretely presented through the\u0000lens of (symmetric monoidal) category theory. In this work, we show how to\u0000formulate fundamental notions of constructor theory within the canvas of\u0000process theory. Specifically, we exploit the functorial interplay between the\u0000symmetric monoidal structure of the category of sets and relations, where the\u0000abstract tasks live, and that of symmetric monoidal categories from physics,\u0000where concrete processes can be found to implement said tasks. Through this, we\u0000answer the question of how constructor theory relates to the broader body of\u0000process-theoretic literature, and provide the impetus for future collaborative\u0000work between the fields.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On periodic solutions and attractors for the Maxwell--Bloch equations 论麦克斯韦-布洛赫方程的周期解和吸引子
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-13 DOI: arxiv-2312.08180
Alexander Komech
{"title":"On periodic solutions and attractors for the Maxwell--Bloch equations","authors":"Alexander Komech","doi":"arxiv-2312.08180","DOIUrl":"https://doi.org/arxiv-2312.08180","url":null,"abstract":"We consider the Maxwell-Bloch system which is a finite-dimensional\u0000approximation of the coupled nonlinear Maxwell-Schr\"odinger equations. The\u0000approximation consists of one-mode Maxwell field coupled to two-level molecule.\u0000We construct time-periodic solutions to the factordynamics which is due to the\u0000symmetry gauge group. For the corresponding solutions to the Maxwell--Bloch\u0000system, the Maxwell field, current and inversion are time-periodic, while the\u0000wave function acquires a unit factor in the period. The proofs rely on\u0000high-amplitude asymptotics of the Maxwell field and a development of suitable\u0000methods of differential topology: the transversality and orientation arguments.\u0000We also prove the existence of the global compact attractor.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138628099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Electrodynamics and Geometric Continuum Mechanics 电动力学和几何连续介质力学
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-13 DOI: arxiv-2312.07978
Reuven Segev
{"title":"Electrodynamics and Geometric Continuum Mechanics","authors":"Reuven Segev","doi":"arxiv-2312.07978","DOIUrl":"https://doi.org/arxiv-2312.07978","url":null,"abstract":"This paper offers an informal instructive introduction to some of the main\u0000notions of geometric continuum mechanics for the case of smooth fields. We use\u0000a metric invariant stress theory of continuum mechanics to formulate a simple\u0000generalization of the fields of electrodynamics and Maxwell's equations to\u0000general differentiable manifolds of any dimension, thus viewing generalized\u0000electrodynamics as a special case of continuum mechanics. The basic kinematic\u0000variable is the potential, which is represented as a $p$-form in an\u0000$n$-dimensional spacetime. The stress for the case of generalized\u0000electrodynamics is assumed to be represented by an $(n-p-1)$-form, a\u0000generalization of the Maxwell $2$-form.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138628090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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