Symmetry is a powerful tool for studying dynamics in QFT as they provide selection rules, constrain RG flows, and allow for simplified dynamics. Currently, our understanding is that the most general form of symmetry is described by categorical symmetries which can be realized via Symmetry TQFTs or ``SymTFTs." In this paper, we show how the framework of the SymTFT, which is understood for discrete symmetries (i.e. finite categorical symmetries), can be generalized to continuous symmetries. In addition to demonstrating how $U(1)$ global symmetries can be incorporated into the paradigm of the SymTFT, we apply our formalism to construct the SymTFT for the $mathbb{Q}/mathbb{Z}$ non-invertible chiral symmetry in $4d$ theories, demonstrate how symmetry fractionalization is realized SymTFTs, and conjecture the SymTFT for general continuous $G^{(0)}$ global symmetries.
{"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":"19 1","pages":""},"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}
Here, we present an algebraic and kinematical analysis of non-commutative $kappa$-Minkowski spaces within Galilean (non-relativistic) and Carrollian (ultra-relativistic) regimes. Utilizing the theory of Wigner-In"{o}nu contractions, we begin with a brief review of how one can apply these contractions to the well-known Poincar'{e} algebra, yielding the corresponding Galilean (both massive and mass-less) and Carrollian algebras as $c to infty$ and $cto 0$, respectively. Subsequently, we methodically apply these contractions to non-commutative $kappa$-deformed spaces, revealing compelling insights into the interplay among the non-commutative parameters $a^mu$ (with $|a^nu|$ being of the order of Planck length scale) and the speed of light $c$ as it approaches both infinity and zero. Our exploration predicts a sort of "branching" of the non-commutative parameters $a^mu$, leading to the emergence of a novel length scale and time scale in either limit. Furthermore, our investigation extends to the examination of curved momentum spaces and their geodesic distances in appropriate subspaces of the $kappa$-deformed Newtonian and Carrollian space-times. We finally delve into the study of their deformed dispersion relations, arising from these deformed geodesic distances, providing a comprehensive understanding of the nature of these space-times.
在此，我们将对伽利略（非相对论）和卡罗尔（超相对论）状态下的非交换$kappa$-闵可夫斯基空间进行代数和运动学分析。利用维格纳-因纽(Wigner-In"{o}nucontractions)理论，我们首先简要回顾了如何将这些contractions应用于著名的Poincar'{e}代数，从而得到相应的伽利略（大质量和无质量）代数和卡罗尔代数，分别为$c to infty$和$c to 0$。随后，我们有条不紊地将这些contractions应用于非交换$kappa$变形空间，揭示了非交换参数$a^mu$（$|a^nu|$是普朗克长度尺度的数量级）与光速$c$之间在接近无穷大和零时的相互作用。我们的探索预测了非交换参数$a^mu$的某种 "分支"，从而导致在任一极限下出现新的长度尺度和时间尺度。此外，我们的研究还扩展到对弯曲动量空间及其在$kappa$变形牛顿时空和卡罗尔时空的适当子空间中的大地距离的考察。最后，我们深入研究了由这些变形测地距离产生的变形色散关系，从而对这些时空的性质有了全面的了解。
{"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":"5 1","pages":""},"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}
We study the boundaries of the positroid cells which arise from N = 4 super Yang Mills theory. Our main tool is a new diagrammatic object which generalizes the Wilson loop diagrams used to represent interactions in the theory. We prove conditions under which these new generalized Wilson loop diagrams correspond to positroids and give an explicit algorithm to calculate the Grassmann necklace of said positroids. Then we develop a graphical calculus operating directly on noncrossing generalized Wilson loop diagrams. In this paradigm, applying diagrammatic moves to a generalized Wilson loop diagram results in new diagrams that represent boundaries of its associated positroid, without passing through cryptomorphisms. We provide a Python implementation of the graphical calculus and use it to show that the boundaries of positroids associated to ordinary Wilson loop diagram are generated by our diagrammatic moves in certain cases.
我们研究了 N = 4 超杨米尔斯理论产生的正方晶胞的边界。我们的主要工具是一种新的图解对象，它概括了理论中用来表示相互作用的威尔逊环图。我们证明了这些新的广义威尔逊环图对应于正子的条件，并给出了计算上述正子的格拉斯曼项链的明确算法。然后，我们开发了一种直接在非交叉广义威尔逊环图上运行的图形微积分。在这种范式中，对广义威尔逊环图应用图解移动，就能得到代表其相关正体边界的新图，而无需通过密码同态。我们提供了图形微积分的 Python 实现，并用它证明了在某些情况下，与普通威尔逊循环图相关的正方体的边界是由我们的图解移动生成的。
{"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":"264 1","pages":""},"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}
We study the configurations of the nearest neighbor Ising ferromagnetic chain with IID centered and square integrable external random field in the limit in which the pairwise interaction tends to infinity. The available free energy estimates for this model show a strong form of disorder relevance, i.e., a strong effect of disorder on the free energy behavior, and our aim is to make explicit how the disorder affects the spin configurations. We give a quantitative estimate that shows that the infinite volume spin configurations are close to one explicit disorder dependent configuration when the interaction is large. Our results confirm the predictions on this model obtained in D. S. Fisher, P. Le Doussal and C. Monthus (Phys. Rev. E 2001) by applying the renormalization group method introduced by D. S. Fisher (Phys. Rev. B 1995).
我们研究了在成对相互作用趋于无穷大的极限条件下，具有以 IID 为中心、可平方积分的外部随机场的近邻 Ising 铁磁链的构型。该模型的现有自由能估计值显示出强烈的无序相关性，即无序对自由能行为的强烈影响，我们的目的是明确无序如何影响自旋构型。我们给出的定量估计表明，当相互作用较大时，无限体积自旋构型接近于一个明确的无序相关构型。我们的结果证实了 D. S. Fisher、P. Le Doussal 和 C. Monthus（Phys. Rev. E 2001）运用 D. S. Fisher（Phys. Rev. B 1995）引入的正则化群方法对该模型的预测。
{"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":"4 1","pages":""},"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}
Stephen A. Wells, Joseph D. Taylor, Paul G. Morris, Alain Nogaret
We construct neuron models from data by transferring information from an observed time series to the state variables and parameters of Hodgkin-Huxley models. When the learning period completes, the model will predict additional observations and its parameters uniquely characterise the complement of ion channels. However, the assimilation of biological data, as opposed to model data, is complicated by the lack of knowledge of the true neuron equations. Reliance on guessed conductance models is plagued with multi-valued parameter solutions. Here, we report on the distributions of parameters and currents predicted with intentionally erroneous models, over-specified models, and an approximate model fitting hippocampal neuron data. We introduce a recursive piecewise data assimilation (RPDA) algorithm that converges with near-perfect reliability when the model is known. When the model is unknown, we show model error introduces correlations between certain parameters. The ionic currents reconstructed from these parameters are excellent predictors of true currents and carry a higher degree of confidence, >95.5%, than underlying parameters, >53%. Unexpressed ionic currents are correctly filtered out even in the presence of mild model error. When the model is unknown, the covariance eigenvalues of parameter estimates are found to be a good gauge of model error. Our results suggest that biological information may be retrieved from data by focussing on current estimates rather than parameters.
{"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":"32 1","pages":""},"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}
We discuss integrable many-body systems in one dimension of Calogero-Moser-Sutherland type, both classical and quantum as well as nonrelativistic and relativistic. In particular, we consider fundamental properties such as integrability, the existence of explicit solutions as well as action-angle and bispectral dualities that relate different such systems. We also briefly discuss the early history of the subject and indicate connections with other integrable systems.
{"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":"48 1","pages":""},"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}
Michael BaakeBielefeld, Anton GorodetskiIrvine, Jan MazáčBielefeld
The aim of this note is to show the existence of a large family of Cantorvals arising in the projection description of primitive two-letter substitutions. This provides a new, naturally occurring class of Cantorvals.
本论文的目的是证明在原始双字母替换的投影描述中存在一个庞大的康托伐尔家族。
{"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":"35 1","pages":""},"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}
Stefano GogiosoHashberg Ltd, Vincent Wang-MaścianicaQuantinuum Ltd, Muhammad Hamza WaseemQuantinuum Ltd, Carlo Maria ScandoloUniversity of Calgary, Bob CoeckeQuantinuum Ltd
Constructor theory is a meta-theoretic approach that seeks to characterise concrete theories of physics in terms of the (im)possibility to implement certain abstract "tasks" by means of physical processes. Process theory, on the other hand, pursues analogous characterisation goals in terms of the compositional structure of said processes, concretely presented through the lens of (symmetric monoidal) category theory. In this work, we show how to formulate fundamental notions of constructor theory within the canvas of process theory. Specifically, we exploit the functorial interplay between the symmetric monoidal structure of the category of sets and relations, where the abstract tasks live, and that of symmetric monoidal categories from physics, where concrete processes can be found to implement said tasks. Through this, we answer the question of how constructor theory relates to the broader body of process-theoretic literature, and provide the impetus for future collaborative work between the fields.
{"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":"5 1","pages":""},"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}
We consider the Maxwell-Bloch system which is a finite-dimensional approximation of the coupled nonlinear Maxwell-Schr"odinger equations. The approximation consists of one-mode Maxwell field coupled to two-level molecule. We construct time-periodic solutions to the factordynamics which is due to the symmetry gauge group. For the corresponding solutions to the Maxwell--Bloch system, the Maxwell field, current and inversion are time-periodic, while the wave function acquires a unit factor in the period. The proofs rely on high-amplitude asymptotics of the Maxwell field and a development of suitable methods of differential topology: the transversality and orientation arguments. We also prove the existence of the global compact attractor.
{"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":"38 1","pages":""},"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}
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the fields of electrodynamics and Maxwell's equations to general differentiable manifolds of any dimension, thus viewing generalized electrodynamics as a special case of continuum mechanics. The basic kinematic variable is the potential, which is represented as a $p$-form in an $n$-dimensional spacetime. The stress for the case of generalized electrodynamics is assumed to be represented by an $(n-p-1)$-form, a generalization of the Maxwell $2$-form.
{"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":"57 1","pages":""},"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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：