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Entropy maximization and weak Gibbsianity of quasi-free fermionic states 准自由费米子态的熵最大化和弱gibbsiity
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-08-21 DOI: 10.1007/s11005-026-02100-9
Vojkan Jakšić, Claude-Alain Pillet, Anna Szczepanek
{"title":"Entropy maximization and weak Gibbsianity of quasi-free fermionic states","authors":"Vojkan Jakšić,&nbsp;Claude-Alain Pillet,&nbsp;Anna Szczepanek","doi":"10.1007/s11005-026-02100-9","DOIUrl":"10.1007/s11005-026-02100-9","url":null,"abstract":"<div><p>In their 1972 study of <i>approach to equilibrium,</i> Lanford and Robinson showed that gauge-invariant quasi-free states of lattice fermions maximize entropy among all translation-invariant states with a fixed two-point function and suggested that the maximizer is unique. In subsequent work on this topic, the uniqueness question re-emerged, together with the problem of whether such quasi-free states are weak Gibbs states. We provide a positive answer to both questions within a class of states whose momentum-space two-point function <span>(widehat{C})</span> satisfies <span>(0&lt;widehat{C}(k)&lt;1)</span> and belongs to the Wiener algebra of the Brillouin zone. The proof reveals that both the entropy maximization principle and weak Gibbsianity follow directly from the thermodynamic formalism for lattice fermions.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02100-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783334","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
Instability of Riemannian Schwarzschild–Tangherlini metrics 黎曼-史瓦西-唐赫里尼度量的不稳定性
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-08-19 DOI: 10.1007/s11005-026-02125-0
Erwann Delay
{"title":"Instability of Riemannian Schwarzschild–Tangherlini metrics","authors":"Erwann Delay","doi":"10.1007/s11005-026-02125-0","DOIUrl":"10.1007/s11005-026-02125-0","url":null,"abstract":"<div><p>We recall a conformal method, suggested in a previous work, for testing the stability of Einstein metrics. We then give a direct application of this method when the manifold is conformal to a Riemannian (multi-)product. Finally, we apply the procedure to the Riemannian Schwarzschild–Tangherlini metric, which turns out to be unstable in dimensions <span>(nin {4,cdots ,9})</span>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782754","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
Conformal blocks, parahoric torsors and Borel–Weil–Bott 共形块，斜体体和Borel-Weil-Bott
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-08-17 DOI: 10.1007/s11005-026-02126-z
Vikraman Balaji, Yashonidhi Pandey
{"title":"Conformal blocks, parahoric torsors and Borel–Weil–Bott","authors":"Vikraman Balaji,&nbsp;Yashonidhi Pandey","doi":"10.1007/s11005-026-02126-z","DOIUrl":"10.1007/s11005-026-02126-z","url":null,"abstract":"<div><p>Let <i>X</i> be a smooth projective curve over a field <i>k</i>. Let <span>(mathcal {G})</span> be a parahoric group scheme on <i>X</i> as in [32]. The aim of this article is to establish the basic themes of the theory of conformal blocks in the parahoric setting. Using Hecke correspondences, we reduce questions on parahoric stacks to those on the reductive (or hyperspecial parahoric) stack via the Iwahori stack. Following this <i>reduction approach</i>, we set-up relationships between the cohomology of line bundles on various moduli stacks of torsors. These relationships give a proof of [32, Conjecture 3.7] in characteristic zero, the principle of propagation of vacua and a direct proof of the independence of central charge on base points. Projective flatness is recovered as a corollary of Faltings’ construction of the Hitchin connection. Using Teleman’s basic results ([38]), we deduce the analogous result that cohomology of line bundles on the stack of principal <i>G</i>-bundles vanishes in all degrees except possibly one over <span>(mathbb {C})</span>. Results on twisted vacua [22] are obtained as immediate consequences.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782499","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
Polynomials and asymptotic constants in a resurgent problem from ’t Hooft t Hooft问题中的多项式和渐近常数
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-08-13 DOI: 10.1007/s11005-026-02135-y
David Broadhurst, Gergő Nemes
{"title":"Polynomials and asymptotic constants in a resurgent problem from ’t Hooft","authors":"David Broadhurst,&nbsp;Gergő Nemes","doi":"10.1007/s11005-026-02135-y","DOIUrl":"10.1007/s11005-026-02135-y","url":null,"abstract":"<div><p>In a recent study of the quantum theory of harmonic oscillators, Gerard ’t Hooft proposed the following problem: given <span>(G(z)=sum _{n=1}^infty sqrt{n},z^n)</span> for <span>(|z|&lt;1)</span>, find its analytic continuation for <span>(|z|ge 1)</span>, excluding a branch-cut <span>(zin [1,,infty ))</span>. A solution is provided by the bilateral convergent sum <span>(G(z)=frac{1}{2}sqrt{pi }sum _{n=-infty }^infty (2pi textrm{i}n-log (z))^{-3/2})</span>. On the negative real axis, <span>(G(-textrm{e}^u))</span> has a sign-constant asymptotic expansion in <span>(1/u^2)</span>, for large positive <i>u</i>. Optimal truncation leaves exponentially suppressed terms in an asymptotic expansion <span>(textrm{e}^{-u}sum _{k=0}^infty P_k(x)/u^k)</span>, with <span>(P_0(x)=x-frac{2}{3})</span> and <span>(P_k(x))</span> of degree <span>(2k+1)</span> evaluated at <span>(x=u/2-lfloor u/2rfloor )</span>. At large <i>k</i>, these polynomials become excellent approximations to sinusoids. The amplitude of <span>(P_k(x))</span> increases factorially with <i>k</i> and its phase increases linearly, with <span>(P_k(x)sim sin ((2k+1)C-2pi x) R^{2k+1}Gamma (k+frac{1}{2})/sqrt{2pi })</span>, where <span>(Capprox 1.0688539158679530121571)</span> and <span>(Rapprox 0.5181839789815558726739)</span> are asymptotic constants satisfying <span>(Rexp (textrm{i},C)=sqrt{-1/(2+pi textrm{i})}.)</span></p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751502","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
Matrix semi-classical Laguerre orthogonal polynomials and non-commutative non-linear equations 矩阵半经典拉盖尔正交多项式和非交换非线性方程
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-08-05 DOI: 10.1007/s11005-026-02121-4
Assil Fradi
{"title":"Matrix semi-classical Laguerre orthogonal polynomials and non-commutative non-linear equations","authors":"Assil Fradi","doi":"10.1007/s11005-026-02121-4","DOIUrl":"10.1007/s11005-026-02121-4","url":null,"abstract":"<div><p>We present the first explicit derivation of a matrix Painlevé IV equation arising from semi-classical matrix orthogonal polynomials of Laguerre-type. Starting from the discrete nonlinear relations for the recurrence coefficients of the associated matrix orthogonal polynomials, established in [9] and identified there as a discrete Painlevé IV equation, we show that the recurrence coefficients satisfy a nonlinear matrix differential-difference equation in the deformation parameter <i>t</i>. These continuous equations provide a natural matrix analogue of the classical Painlevé IV equation, reducing to the scalar case when all coefficients commute. We conclude with a new concrete asymmetric low-dimensional example illustrating the main result.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750748","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
Clifford algebras, meson algebras and higher order generalizations Clifford代数，介子代数和高阶推广
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-08-04 DOI: 10.1007/s11005-026-02132-1
Michel Dubois-Violette, Blas Torrecillas
{"title":"Clifford algebras, meson algebras and higher order generalizations","authors":"Michel Dubois-Violette,&nbsp;Blas Torrecillas","doi":"10.1007/s11005-026-02132-1","DOIUrl":"10.1007/s11005-026-02132-1","url":null,"abstract":"<div><p>We analyse the homogeneous parts of Clifford and meson algebras and point out that for the Clifford algebra it is related to fermionic statistics, that is, to fermionic parastatistics of order 1 while for the meson algebra it is related to fermionic parastatistics of order 2. We extend these homogeneous algebras into corresponding algebras related to fermionic parastatistics of all orders. We then define correspondingly higher order generalizations of Clifford and meson algebras.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750562","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
Integrability from categorification and higher Kac–Moody algebras 范畴代数与高Kac-Moody代数的可积性
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-08-04 DOI: 10.1007/s11005-026-02129-w
Hank Chen, Florian Girelli
{"title":"Integrability from categorification and higher Kac–Moody algebras","authors":"Hank Chen,&nbsp;Florian Girelli","doi":"10.1007/s11005-026-02129-w","DOIUrl":"10.1007/s11005-026-02129-w","url":null,"abstract":"<div><p>The theory of Lie bialgebras and the classical Yang–Baxter equation plays a major role in the study of 1+1d integrable systems; many families of integrable systems can be recovered from a Lax pair which is constructed from a Lie bialgebra. A categorified, higher homotopy notion of Lie algebras has been studied, which gave rise to the notion of (strict) Lie 2-bialgebras (Lie algebra crossed-modules) and the 2-graded Yang–Baxter equations. In this paper, we use these differential-graded structures to generalize the construction of a Lax pair and introduce an appropriate notion of higher-dimensional integrability. Within this framework, we introduce a higher derived version of the affine Kac–Moody algebra, which underpins the 2-graded Lax integrability that we have developed here as a zero 2-curvature condition. As an explicit demonstration, we will consider a 3d field theory and show that it (i) is 2-graded Lax integrable and (ii) hosts symmetries governed by a Kac–Moody 2-algebra.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750598","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
Nonlinear Lie conformal algebras and one-loop corrections of self-dual Yang–Mills amplitudes 非线性李共形代数与自对偶Yang-Mills振幅的单环修正
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-08-01 DOI: 10.1007/s11005-026-02131-2
Charles Igel, Jeremy Mancinas, Juan Villarreal
{"title":"Nonlinear Lie conformal algebras and one-loop corrections of self-dual Yang–Mills amplitudes","authors":"Charles Igel,&nbsp;Jeremy Mancinas,&nbsp;Juan Villarreal","doi":"10.1007/s11005-026-02131-2","DOIUrl":"10.1007/s11005-026-02131-2","url":null,"abstract":"<div><p>This work is motivated by recent developments in celestial holography. In [15], the authors interpreted QCD collinear singularities in terms of operator product expansions in a two-dimensional CFT. We reformulate the algebraic structures arising in their work using the formalism of nonlinear Lie conformal algebras developed in [31].\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02131-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628457","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
On the discrete Painlevé equivalence problem, non-conjugate translations and nodal curves 关于离散painlevevl等价问题，非共轭平移和节点曲线
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-08-01 DOI: 10.1007/s11005-026-02117-0
Anton Dzhamay, Galina Filipuk, Alexander Stokes
{"title":"On the discrete Painlevé equivalence problem, non-conjugate translations and nodal curves","authors":"Anton Dzhamay,&nbsp;Galina Filipuk,&nbsp;Alexander Stokes","doi":"10.1007/s11005-026-02117-0","DOIUrl":"10.1007/s11005-026-02117-0","url":null,"abstract":"<div><p>We consider several examples of nonautonomous systems of difference equations coming from semi-classical orthogonal polynomials via recurrence coefficients and ladder operators, with respect to various generalisations of Laguerre and Meixner weights. We identify these as discrete Painlevé equations and establish their types in the Sakai classification scheme in terms of the associated rational surfaces. In particular, we find examples which come from different weights and share a common surface type <span>(D_5^{(1)})</span> but are inequivalent in two ways. First, their dynamics are generated by non-conjugate elements of <span>(widehat{W}(A_3^{(1)}))</span>. Second, some of the examples have associated surfaces being non-generic in the sense of having nodal curves. The symmetries of these examples form subgroups of the generic symmetry group, which we compute. In particular, we find <span>((W(A_1^{(1)})times W(A_1^{(1)}))rtimes mathbb {Z}/2mathbb {Z})</span>. These examples give further weight to the argument that any correspondence between different weights and the Sakai classification should make use of the refined version of the discrete Painlevé equivalence problem, which takes into account not just surface type, but also the group elements generating the dynamics as well as parameter constraints, e.g. those corresponding to nodal curves.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02117-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628456","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
Representations of the flat space wavefunction 平面空间波函数的表示
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-07-29 DOI: 10.1007/s11005-026-02128-x
Tyler Dunaisky
{"title":"Representations of the flat space wavefunction","authors":"Tyler Dunaisky","doi":"10.1007/s11005-026-02128-x","DOIUrl":"10.1007/s11005-026-02128-x","url":null,"abstract":"<div><p>From any graph <i>G</i> arises a flat space wavefunction, obtained by integrating a product of propagatorsassociated to the vertices and edges of <i>G</i>. This function is a key ingredient in the computation of cosmological correlators, and several representations for it have been proposed. We formulate three such representations and prove their correctness. In particular, we show that the flat space wavefunction can be read off from the canonical form of the cosmological polytope, and we settle a conjecture of Fevola, Pimentel, Sattelberger, and Westerdijk regarding a partial fraction decomposition for the flat space wavefunction. The terms of the decomposition correspond to certain collections of connected subgraphs associated to <i>G</i> and its spanning subgraphs, reflecting the fact that the flat space wavefunction contains information about how <i>G</i> is connected.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02128-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615063","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
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