Symmetry Integrability and Geometry-Methods and Applications最新文献_第2页

Packing Densities of Delzant and Semitoric Polygons 三角多边形和半三角多边形的填充密度

3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-29 DOI: 10.3842/sigma.2023.081

Du, Yu, Kosmacher, Gabriel, Liu, Yichen, Massman, Jeff, Palmer, Joseph, Thieme, Timothy, Wu, Jerry, Zhang, Zheyu

引用次数: 0

A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation 第三阶painlevleve方程Umemura多项式的构造证明

3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-25 DOI: 10.3842/sigma.2023.080

Peter A. Clarkson, Chun-Kong Law, Chia-Hua Lin

引用次数: 2

Information Geometry, Jordan Algebras, and a Coadjoint Orbit-Like Construction 信息几何、约当代数和协同类轨道构造

3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-20 DOI: 10.3842/sigma.2023.078

Florio M. Ciaglia, Jürgen Jost, Lorenz J. Schwachhöfer

{"title":"Information Geometry, Jordan Algebras, and a Coadjoint Orbit-Like Construction","authors":"Florio M. Ciaglia, Jürgen Jost, Lorenz J. Schwachhöfer","doi":"10.3842/sigma.2023.078","DOIUrl":"https://doi.org/10.3842/sigma.2023.078","url":null,"abstract":"Jordan algebras arise naturally in (quantum) information geometry, and we want to understand their role and their structure within that framework. Inspired by Kirillov's discussion of the symplectic structure on coadjoint orbits, we provide a similar construction in the case of real Jordan algebras. Given a real, finite-dimensional, formally real Jordan algebra ${mathcal J}$, we exploit the generalized distribution determined by the Jordan product on the dual ${mathcal J}^{star}$ to induce a pseudo-Riemannian metric tensor on the leaves of the distribution. In particular, these leaves are the orbits of a Lie group, which is the structure group of ${mathcal J}$, in clear analogy with what happens for coadjoint orbits. However, this time in contrast with the Lie-algebraic case, we prove that not all points in ${mathcal J}^{*}$ lie on a leaf of the canonical Jordan distribution. When the leaves are contained in the cone of positive linear functionals on ${mathcal J}$, the pseudo-Riemannian structure becomes Riemannian and, for appropriate choices of ${mathcal J}$, it coincides with the Fisher-Rao metric on non-normalized probability distributions on a finite sample space, or with the Bures-Helstrom metric for non-normalized, faithful quantum states of a finite-level quantum system, thus showing a direct link between the mathematics of Jordan algebras and both classical and quantum information geometry.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617764","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: 4

About a Family of ALF Instantons with Conical Singularities 关于一类具有圆锥奇异点的ALF实例

3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-20 DOI: 10.3842/sigma.2023.079

Olivier Biquard, Paul Gauduchon

引用次数: 1

Tensors and Algebras: An Algebraic Spacetime Interpretation for Tensor Models 张量与代数:张量模型的代数时空解释

3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-18 DOI: 10.3842/sigma.2023.076

Dennis Obster

{"title":"Tensors and Algebras: An Algebraic Spacetime Interpretation for Tensor Models","authors":"Dennis Obster","doi":"10.3842/sigma.2023.076","DOIUrl":"https://doi.org/10.3842/sigma.2023.076","url":null,"abstract":"The quest for a consistent theory for quantum gravity is one of the most challenging problems in theoretical high-energy physics. An often-used approach is to describe the gravitational degrees of freedom by the metric tensor or related variables, and finding a way to quantise this. In the canonical tensor model, the gravitational degrees of freedom are encoded in a tensorial quantity $P_{abc}$, and this quantity is subsequently quantised. This makes the quantisation much more straightforward mathematically, but the interpretation of this tensor as a spacetime is less evident. In this work we take a first step towards fully understanding the relationship to spacetime. By considering $P_{abc}$ as the generator of an algebra of functions, we first describe how we can recover the topology and the measure of a compact Riemannian manifold. Using the tensor rank decomposition, we then generalise this principle in order to have a well-defined notion of the topology and geometry for a large class of tensors $P_{abc}$. We provide some examples of the emergence of a topology and measure of both exact and perturbed Riemannian manifolds, and of a purely algebraically-defined space called the semi-local circle.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135883909","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: 3

The Higher-Rank Askey-Wilson Algebra and Its Braid Group Automorphisms 高阶Askey-Wilson代数及其辫群自同构

3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-18 DOI: 10.3842/sigma.2023.077

Nicolas Crampe, Luc Frappat, Loic Poulain d'Andecy, Eric Ragoucy

{"title":"The Higher-Rank Askey-Wilson Algebra and Its Braid Group Automorphisms","authors":"Nicolas Crampe, Luc Frappat, Loic Poulain d'Andecy, Eric Ragoucy","doi":"10.3842/sigma.2023.077","DOIUrl":"https://doi.org/10.3842/sigma.2023.077","url":null,"abstract":"We propose a definition by generators and relations of the rank $n-2$ Askey-Wilson algebra $mathfrak{aw}(n)$ for any integer $n$, generalising the known presentation for the usual case $n=3$. The generators are indexed by connected subsets of ${1,dots,n}$ and the simple and rather small set of defining relations is directly inspired from the known case of $n=3$. Our first main result is to prove the existence of automorphisms of $mathfrak{aw}(n)$ satisfying the relations of the braid group on $n+1$ strands. We also show the existence of coproduct maps relating the algebras for different values of $n$. An immediate consequence of our approach is that the Askey-Wilson algebra defined here surjects onto the algebra generated by the intermediate Casimir elements in the $n$-fold tensor product of the quantum group ${rm U}_q(mathfrak{sl}_2)$ or, equivalently, onto the Kauffman bracket skein algebra of the $(n+1)$-punctured sphere. We also obtain a family of central elements of the Askey-Wilson algebras which are shown, as a direct by-product of our construction, to be sent to $0$ in the realisation in the $n$-fold tensor product of ${rm U}_q(mathfrak{sl}_2)$, thereby producing a large number of relations for the algebra generated by the intermediate Casimir elements.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823497","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

Sun's Series via Cyclotomic Multiple Zeta Values 太阳的系列通过环切多重Zeta值

3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-12 DOI: 10.3842/sigma.2023.074

Yajun Zhou

引用次数: 1

Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras Dijkgraaf-Witten范畴的Frobenius一元函子和刚性Frobenius代数

3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-12 DOI: 10.3842/sigma.2023.075

Samuel Hannah, Robert Laugwitz, Ana Ros Camacho

引用次数: 0

Nudged Elastic Bands and Lightly Bound Skyrmions 轻推松紧带和轻绑Skyrmions

3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-11 DOI: 10.3842/sigma.2023.073

James Martin Speight, Thomas Winyard

{"title":"Nudged Elastic Bands and Lightly Bound Skyrmions","authors":"James Martin Speight, Thomas Winyard","doi":"10.3842/sigma.2023.073","DOIUrl":"https://doi.org/10.3842/sigma.2023.073","url":null,"abstract":"It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon number) $B$. Rigid body quantization, in which one quantizes motion on the spin-isospin orbit of just one minimum, is thus an ill-justified approximation. Instead, one should identify a (finite-dimensional) moduli space of configurations containing all local minima (for a given $B$) as well as fields interpolating smoothly between them. This paper proposes a systematic computational scheme for generating such a moduli space: one constructs an energy minimizing path between each pair of local minima, then defines the moduli space to be the union of spin-isospin orbits of points on the union of these curves, a principal bundle over a graph. The energy minimizing curves may be constructed in practice using the nudged elastic band method, a standard tool in mathematical chemistry for analyzing reaction paths and computing activation energies. To illustrate, we apply this scheme to the lightly bound Skyrme model in the point particle approximation, constructing the graphs for $5leq Bleq 10$. We go on to complete the quantization for $B=7$, in which the graph has two vertices and a single edge. The low-lying quantum states with isospin $1/2$ do not strongly localize around either of the local energy minima (the vertices). Their energies rise monotonically with spin, conflicting with experimental data for Lithium-7.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"198 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136208632","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: 1

Multiplicative Characters and Gaussian Fluctuation Limits 乘法性质与高斯涨落极限

3区物理与天体物理

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-03 DOI: 10.3842/sigma.2023.072

Ryosuke Sato

引用次数: 0