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Algorithm for differential equations for Feynman integrals in general dimensions 一般维度费曼积分微分方程算法
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-06-26 DOI: 10.1007/s11005-024-01832-w
Leonardo de la Cruz, Pierre Vanhove
{"title":"Algorithm for differential equations for Feynman integrals in general dimensions","authors":"Leonardo de la Cruz,&nbsp;Pierre Vanhove","doi":"10.1007/s11005-024-01832-w","DOIUrl":"10.1007/s11005-024-01832-w","url":null,"abstract":"<div><p>We present an algorithm for determining the minimal order differential equations associated with a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths–Dwork pole reduction adapted to the case of twisted differential forms. In dimensional regularisation, we demonstrate the applicability of this algorithm by explicitly providing the inhomogeneous differential equations for the multi-loop two-point sunset integrals: up to 20 loops for the equal-mass case, the generic mass case at two- and three-loop orders. Additionally, we derive the differential operators for various infrared-divergent two-loop graphs. In the analytic regularisation case, we apply our algorithm for deriving a system of partial differential equations for regulated Witten diagrams, which arise in the evaluation of cosmological correlators of conformally coupled <span>(phi ^4)</span> theory in four-dimensional de Sitter space.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506225","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
When quantum memory is useful for dense coding 量子存储器何时可用于密集编码
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-06-22 DOI: 10.1007/s11005-024-01831-x
Ryuji Takagi, Masahito Hayashi
{"title":"When quantum memory is useful for dense coding","authors":"Ryuji Takagi,&nbsp;Masahito Hayashi","doi":"10.1007/s11005-024-01831-x","DOIUrl":"10.1007/s11005-024-01831-x","url":null,"abstract":"<div><p>We discuss dense coding with <i>n</i> copies of a specific preshared state between the sender and the receiver when the encoding operation is limited to the application of group representation. Typically, to act on multiple local copies of these preshared states, the receiver needs quantum memory, because in general the multiple copies will be generated sequentially. Depending on available encoding unitary operations, we investigate what preshared state offers an advantage of using quantum memory on the receiver’s side.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506227","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
D-module techniques for solving differential equations in the context of Feynman integrals 费曼积分背景下求解微分方程的 D 模块技术
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-06-21 DOI: 10.1007/s11005-024-01835-7
Johannes Henn, Elizabeth Pratt, Anna-Laura Sattelberger, Simone Zoia
{"title":"D-module techniques for solving differential equations in the context of Feynman integrals","authors":"Johannes Henn,&nbsp;Elizabeth Pratt,&nbsp;Anna-Laura Sattelberger,&nbsp;Simone Zoia","doi":"10.1007/s11005-024-01835-7","DOIUrl":"10.1007/s11005-024-01835-7","url":null,"abstract":"<div><p>Feynman integrals are solutions to linear partial differential equations with polynomial coefficients. Using a triangle integral with general exponents as a case in point, we compare <i>D</i>-module methods to dedicated methods developed for solving differential equations appearing in the context of Feynman integrals, and provide a dictionary of the relevant concepts. In particular, we implement an algorithm due to Saito, Sturmfels, and Takayama to derive canonical series solutions of regular holonomic <i>D</i>-ideals, and compare them to asymptotic series derived by the respective Fuchsian systems.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01835-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506226","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
Geometry of entanglement and separability in Hilbert subspaces of dimension up to three 三维以内希尔伯特子空间中的纠缠几何与可分性
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-06-21 DOI: 10.1007/s11005-024-01816-w
Rotem Liss, Tal Mor, Andreas Winter
{"title":"Geometry of entanglement and separability in Hilbert subspaces of dimension up to three","authors":"Rotem Liss,&nbsp;Tal Mor,&nbsp;Andreas Winter","doi":"10.1007/s11005-024-01816-w","DOIUrl":"10.1007/s11005-024-01816-w","url":null,"abstract":"<div><p>We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding the geometric structure of the pure product states in a given three-dimensional Hilbert subspace, which determines all the possible separable and entangled mixed states over the same subspace. In bipartite systems, we characterise the 14 possible qualitatively different geometric shapes for the set of separable states in any three-dimensional Hilbert subspace (5 classes which also appear in two-dimensional subspaces and were found and analysed by Boyer et al. (Phys Rev A 95:032308, 2017. https://doi.org/10.1103/PhysRevA.95.032308), and 9 novel classes which appear only in three-dimensional subspaces), describe their geometries, and provide figures illustrating them. We also generalise these results to characterise the sets of fully separable states (and hence the complementary sets of somewhat entangled states) in three-dimensional subspaces of multipartite systems. Our results show which geometrical forms quantum entanglement can and cannot take in low-dimensional subspaces.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01816-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532370","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
Geometrization of the TUY/WZW/KZ connection TUY/WZW/KZ 连接的几何结构
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-06-21 DOI: 10.1007/s11005-024-01834-8
Indranil Biswas, Swarnava Mukhopadhyay, Richard Wentworth
{"title":"Geometrization of the TUY/WZW/KZ connection","authors":"Indranil Biswas,&nbsp;Swarnava Mukhopadhyay,&nbsp;Richard Wentworth","doi":"10.1007/s11005-024-01834-8","DOIUrl":"10.1007/s11005-024-01834-8","url":null,"abstract":"<div><p>Given a simple, simply connected, complex algebraic group <i>G</i>, a flat projective connection on the bundle of non-abelian theta functions on the moduli space of semistable parabolic <i>G</i>-bundles over any family of smooth projective curves with marked points was constructed by the authors in an earlier paper. Here, it is shown that the identification between the bundle of non-abelian theta functions and the bundle of WZW conformal blocks is flat with respect to this connection and the one constructed by Tsuchiya–Ueno–Yamada. As an application, we give a geometric construction of the Knizhnik–Zamolodchikov connection on the trivial bundle over the configuration space of points in the projective line whose typical fiber is the space of invariants of tensor product of representations.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512719","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
Correction: Volume singularities in general relativity 更正：广义相对论中的体积奇点
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-06-20 DOI: 10.1007/s11005-024-01838-4
Leonardo García-Heveling
{"title":"Correction: Volume singularities in general relativity","authors":"Leonardo García-Heveling","doi":"10.1007/s11005-024-01838-4","DOIUrl":"10.1007/s11005-024-01838-4","url":null,"abstract":"","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01838-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412661","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
Long-time asymptotics for a complex cubic Camassa–Holm equation 复立方卡马萨-霍尔姆方程的长时渐近线
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-06-20 DOI: 10.1007/s11005-024-01833-9
Hongyi Zhang, Yufeng Zhang, Binlu Feng
{"title":"Long-time asymptotics for a complex cubic Camassa–Holm equation","authors":"Hongyi Zhang,&nbsp;Yufeng Zhang,&nbsp;Binlu Feng","doi":"10.1007/s11005-024-01833-9","DOIUrl":"10.1007/s11005-024-01833-9","url":null,"abstract":"<div><p>In this paper, we investigate the Cauchy problem of the following complex cubic Camassa–Holm equation </p><div><div><span>$$begin{aligned} m_{t}=bu_{x}+frac{1}{2}left[ mleft( |u|^{2}-left| u_{x}right| ^{2}right) right] _{x}-frac{1}{2} mleft( u bar{u}_{x}-u_{x} bar{u}right) , quad m=u-u_{x x}, end{aligned}$$</span></div></div><p>where <span>(b&gt;0)</span> is an arbitrary positive real constant. Long-time asymptotics of the equation is obtained through the <span>(bar{partial })</span>-steepest descent method. Firstly, based on the spectral analysis of the Lax pair and scattering matrix, the solution of the equation is able to be constructed via solving the corresponding Riemann–Hilbert problem. Then, we present different long-time asymptotic expansions of the solution <i>u</i>(<i>y</i>, <i>t</i>) in different space-time solitonic regions of <span>(xi =y/t)</span>. The half-plane <span>({(y,t):-infty&lt;y&lt; infty , t &gt; 0})</span> is divided into four asymptotic regions: <span>(xi in (-infty ,-1))</span>, <span>(xi in (-1,0))</span>, <span>(xi in (0,frac{1}{8}))</span> and <span>(xi in (frac{1}{8},+infty ))</span>. When <span>(xi )</span> falls in <span>((-infty ,-1)cup (frac{1}{8},+infty ))</span>, no stationary phase point of the phase function <span>(theta (z))</span> exists on the jump profile in the space-time region. In this case, corresponding asymptotic approximations can be characterized with an <span>(N(Lambda ))</span>-solitons with diverse residual error order <span>(O(t^{-1+2varepsilon }))</span>. There are four stationary phase points and eight stationary phase points on the jump curve as <span>(xi in (-1,0))</span> and <span>(xi in (0,frac{1}{8}))</span>, respectively. The corresponding asymptotic form is accompanied by a residual error order <span>(O(t^{-frac{3}{4}}))</span>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512721","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
Vertex operators of the KP hierarchy and singular algebraic curves KP 层次的顶点算子和奇异代数曲线
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-06-19 DOI: 10.1007/s11005-024-01836-6
Atsushi Nakayashiki
{"title":"Vertex operators of the KP hierarchy and singular algebraic curves","authors":"Atsushi Nakayashiki","doi":"10.1007/s11005-024-01836-6","DOIUrl":"10.1007/s11005-024-01836-6","url":null,"abstract":"<div><p>Quasi-periodic solutions of the KP hierarchy acted by vertex operators are studied. We show, with the aid of the Sato Grassmannian, that solutions thus constructed correspond to torsion free rank one sheaves on some singular algebraic curves whose normalizations are the non-singular curves corresponding to the seed quasi-periodic solutions. It means that the action of the vertex operator has an effect of creating singular points on an algebraic curve. We further check, by examples, that solutions obtained here can be considered as solitons on quasi-periodic backgrounds, where the soliton matrices are determined by parameters in the vertex operators.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512720","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
Attractor flow versus Hesse flow in wall-crossing structures 穿墙结构中的吸引流与黑塞流
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-06-08 DOI: 10.1007/s11005-024-01830-y
Qiang Wang
{"title":"Attractor flow versus Hesse flow in wall-crossing structures","authors":"Qiang Wang","doi":"10.1007/s11005-024-01830-y","DOIUrl":"10.1007/s11005-024-01830-y","url":null,"abstract":"<div><p>We recast the physics discussions in the paper of Van den Bleeken (J High Energy Phys 2012(2):67, 2012) within the context of wall-crossing structure à la Kontsevich and Soibelman (Homol Mirror Symmetry Trop Geom, 2014. https://doi.org/10.1007/978-3-319-06514-4_6). In particular, we compare the Hesse flow given in Van den Bleeken (J High Energy Phys 2012(2):67, 2012) and the attractor flow on the base of the complex integrable system, and show that both can be used in the formalism of wall-crossing structure. We also propose the notions of dual Hesse flow and dual attractor flow, and show that under the rotation of the <span>(mathbb {Z})</span>-affine structure, the Hesse flow can be transformed into the dual attractor flow, while the attractor flow into the dual Hesse flow. This suggests its possible use in Mirror Symmetry.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141370011","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
Usefulness of signed eigenvalue/vector distributions of random tensors 随机张量的符号特征值/向量分布的用途
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-06-07 DOI: 10.1007/s11005-024-01825-9
Max Regalado Kloos, Naoki Sasakura
{"title":"Usefulness of signed eigenvalue/vector distributions of random tensors","authors":"Max Regalado Kloos,&nbsp;Naoki Sasakura","doi":"10.1007/s11005-024-01825-9","DOIUrl":"10.1007/s11005-024-01825-9","url":null,"abstract":"<div><p>Quantum field theories can be applied to compute various statistical properties of random tensors. In particular, signed distributions of tensor eigenvalues/vectors are the easiest, which can be computed as partition functions of four-fermi theories. Though signed distributions are different from genuine ones because of extra signs of weights, they are expected to coincide in vicinities of ends of distributions. In this paper, we perform a case study of the signed eigenvalue/vector distribution of the real symmetric order-three random tensor. The correct critical point and the correct end in the large <i>N</i> limit are obtained from the four-fermi theory, for which a method using the Schwinger-Dyson equation is very efficient. Since locations of ends are particularly important in applications, such as the largest eigenvalues and the best rank-one tensor approximations, signed distributions are the easiest and highly useful through the Schwinger-Dyson method.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548736","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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