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Open strings on knot complements 结补上的开弦
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-11-05 DOI: 10.1007/s11005-026-02183-4
Sachin Chauhan, Tobias Ekholm, Pietro Longhi
{"title":"Open strings on knot complements","authors":"Sachin Chauhan,&nbsp;Tobias Ekholm,&nbsp;Pietro Longhi","doi":"10.1007/s11005-026-02183-4","DOIUrl":"10.1007/s11005-026-02183-4","url":null,"abstract":"<div><p>Using skein-valued holomorphic curve counting techniques, we give a flow loop formula for the skein-valued partition function of the Lagrangian knot complement of a fibered knot (of the <i>A</i>-model open topological strings with Lagrangian <i>A</i>-branes wrapping the complement) in the cotangent bundle of the three-sphere and in the resolved conifold. For torus knots, we show that the partition function in the cotangent bundle localizes on two or three holomorphic annuli and give a corresponding generalized quiver structure for the partition function in the resolved conifold. We connect the formula to the augmentation curve, the representation variety of the knot contact homology algebra of the knot, generated by Reeb chords of its Legendrian conormal and with differential given by holomorphic disks interpolating between words of Reeb chords. The curve admits a quantization as a <i>q</i>-difference equation for the generating function of symmetrically colored HOMFLYPT-polynomials of the knot or, geometrically, for the <i>U</i>(1)-partition function of the knot conormal. For <span>((2,2p+1))</span>-torus knots, we show that, after a change of variables, the partition function of the knot complement also satisfies this <i>q</i>-difference equation. This gives another geometrically defined coordinate chart for the <i>D</i>-module defined by the quantized augmentation polynomial.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02183-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149338310","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
Relativistic Dirac Landau levels in Snyder–de Sitter space: shape invariance and the reality-fixed mixing parameter Snyder-de Sitter空间中的相对论狄拉克朗道能级：形状不变性和现实固定的混合参数
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-31 DOI: 10.1007/s11005-026-02181-6
Florent Degbo, Finagnon A. Dossa, Gabriel Y. H. Avossevou
{"title":"Relativistic Dirac Landau levels in Snyder–de Sitter space: shape invariance and the reality-fixed mixing parameter","authors":"Florent Degbo,&nbsp;Finagnon A. Dossa,&nbsp;Gabriel Y. H. Avossevou","doi":"10.1007/s11005-026-02181-6","DOIUrl":"10.1007/s11005-026-02181-6","url":null,"abstract":"<div><p>We exactly solve the two-dimensional Dirac equation for a charged particle subject to a uniform magnetic field in the noncommutative Snyder–de Sitter space, whose algebra combines coordinate noncommutativity with a curvature of momentum space. Working in the momentum-space differential representation, and keeping a mixing parameter <span>(lambda )</span> free up to the spectral stage, we derive the associated second-order radial equation and then eliminate its first-derivative term to bring it to the form of an effective Schrödinger-type Hamiltonian. This Hamiltonian is factorized within the framework of supersymmetric quantum mechanics and is shown to be shape invariant under a simple translation of its parameters, which allows the energy spectrum and eigenstates to be obtained analytically. We show that the requirement of a real spectrum uniquely fixes the value of the parameter <span>(lambda )</span>. The commutative, pure Snyder, and pure de Sitter limits are examined explicitly, both for the energy levels and for the wave functions, which are expressed in terms of Jacobi polynomials reducing to the generalized Laguerre polynomials of the usual Landau levels.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339644","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
Numerical approach to the modular operator for fermionic systems 费米子系统模算子的数值方法
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-30 DOI: 10.1007/s11005-026-02175-4
Henning Bostelmann, Daniela Cadamuro, Christoph Minz
{"title":"Numerical approach to the modular operator for fermionic systems","authors":"Henning Bostelmann,&nbsp;Daniela Cadamuro,&nbsp;Christoph Minz","doi":"10.1007/s11005-026-02175-4","DOIUrl":"10.1007/s11005-026-02175-4","url":null,"abstract":"<div><p>We numerically approximate the Tomita–Takesaki modular operator for local subalgebras of the 1+1-dimensional massive Majorana field. Our method works at the one-particle level with a discretisation of time-0 data in position space. The local subspaces we consider are associated with one double cone and with the disjoint union of two double cones. In order to avoid boundary effects, we primarily choose the overall spacetime to be a cylinder; different choices of boundary conditions (antiperiodic and periodic) are considered. We compare our numerical results to known analytic expressions in the massless case. It turns out that the modular operator has a non-trivial dependence on the mass. In the case of two double cones, the modular generator does not only have ”local” contributions (supported on the diagonal in configuration space) but also ”bilocal” terms (connecting the two double cone regions); we find the latter to be less prominent at higher masses, in line with expectations.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02175-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339529","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
Vacuum and thermal fluctuations of a scalar field with point interactions 具有点相互作用的标量场的真空和热涨落
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-30 DOI: 10.1007/s11005-026-02180-7
Davide Fermi, Marco Gurgoglione
{"title":"Vacuum and thermal fluctuations of a scalar field with point interactions","authors":"Davide Fermi,&nbsp;Marco Gurgoglione","doi":"10.1007/s11005-026-02180-7","DOIUrl":"10.1007/s11005-026-02180-7","url":null,"abstract":"<div><p>We investigate the vacuum and thermal fluctuations of a neutral massless scalar field living in Minkowski spacetime and interacting with a finite number of point-like obstacles, modelled by zero-range potentials. The system is described rigorously in terms of self-adjoint realizations of the Laplacian, under assumptions ensuring the absence of instabilities. Using the relative zeta-function technique, we determine the renormalized connected partition function and derive explicit expressions for the thermodynamic observables, characterizing both their low- and high-temperature behaviors. Furthermore, we derive of a convergent Born series expansion for the Casimir energy, which identifies multiple-scattering processes as the mechanism underlying vacuum forces. The latter decompose into pairwise contributions directed along the lines joining the obstacles, with intensities depending non-locally on the full configuration. We also present some numerical results for identical obstacles, indicating that the Casimir forces are always attractive in this context.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339226","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
Profile dimensions and endpoint Lorentz laws for power-law quasiperiodic localization 幂律拟周期局部化的轮廓尺寸和端点洛伦兹定律
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-29 DOI: 10.1007/s11005-026-02179-0
Xingkui Shu
{"title":"Profile dimensions and endpoint Lorentz laws for power-law quasiperiodic localization","authors":"Xingkui Shu","doi":"10.1007/s11005-026-02179-0","DOIUrl":"10.1007/s11005-026-02179-0","url":null,"abstract":"<div><p>We study the phase distribution of localization constants for quasiperiodic lattice operators with power-law long-range hopping. The central idea is a profile-to-Lorentz transference principle: a quantitative small-value law for a resonance depth yields a weak-Lorentz upper bound for every localization quantity controlled pointwise by that depth. When the depth itself has a two-sided power-law small-value distribution, the associated power depth has an exact weak-Lorentz critical index. Applying this mechanism to the power-law localization theorem of Shi and Wen, we prove an endpoint phase-distribution estimate for the dynamical localization constant. The exponent is governed by the Diophantine exponent of the frequency and by the algebraic exponent in the Green function estimate. We also formulate a unified profile principle in which quantitative scalar sublevel estimates determine Lorentz upper bounds. The operator conclusion is stated under an explicit Green-function profile bound, so the metric input and the operator input remain logically separate.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339484","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
The Fock Space Dynamics of Causal Fermion Systems: Non-Abelian Gauge Fields 因果费米子系统的Fock空间动力学：非阿贝尔规范场
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-27 DOI: 10.1007/s11005-026-02178-1
Claudio Dappiaggi, Felix Finster, Niky Kamran, Moritz Reintjes
{"title":"The Fock Space Dynamics of Causal Fermion Systems: Non-Abelian Gauge Fields","authors":"Claudio Dappiaggi,&nbsp;Felix Finster,&nbsp;Niky Kamran,&nbsp;Moritz Reintjes","doi":"10.1007/s11005-026-02178-1","DOIUrl":"10.1007/s11005-026-02178-1","url":null,"abstract":"<div><p>A limiting case is worked out in which the causal action principle for causal fermion systems describing Minkowski space gives rise to the linear Fock space dynamics of perturbative quantum field theory, including non-abelian gauge fields and Dirac fields.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02178-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149338770","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 semisimplicity and Schur elements of (super)symmetric superalgebras （超）对称超代数的半简单性和Schur元
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-22 DOI: 10.1007/s11005-026-02165-6
Lei Shi
{"title":"On the semisimplicity and Schur elements of (super)symmetric superalgebras","authors":"Lei Shi","doi":"10.1007/s11005-026-02165-6","DOIUrl":"10.1007/s11005-026-02165-6","url":null,"abstract":"<div><p>In this paper, we use Schur elements to derive semisimplicity criteria for (super) symmetric superalgebras. We obtain a closed formula for the Schur elements of cyclotomic Hecke–Clifford superalgebras <span>(mathcal {H}^{f}_{mathbb {K}})</span>. As applications, we prove that two trace functions <span>(gimel _n)</span> and <span>(t_{1,n})</span> on the Hecke–Clifford superalgebra, which are defined in different ways, are proportional. We give a semisimplicity criterion for <span>(mathcal {H}^{f}_{mathbb {K}})</span> when it is (super)symmetric. We also derive semisimplicity criteria for cyclotomic quiver Hecke superalgebras of types <span>(A^{(1)}_{e})</span>, <span>(C^{(1)}_{e})</span>, <span>(A^{(2)}_{2e})</span> and <span>(D^{(2)}_{e+1})</span>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02165-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149234771","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
Correction: A coassociative C*-quantum group with nonintegral dimensions 修正：一个非整维的协协C*量子群
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-20 DOI: 10.1007/s11005-026-02151-y
Gabriella Böhm, Kornél Szlachányi
{"title":"Correction: A coassociative C*-quantum group with nonintegral dimensions","authors":"Gabriella Böhm,&nbsp;Kornél Szlachányi","doi":"10.1007/s11005-026-02151-y","DOIUrl":"10.1007/s11005-026-02151-y","url":null,"abstract":"","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149234331","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
Long-time asymptotics of the autocorrelation function of the transverse Ising chain at the critical magnetic field revisited 重新讨论了临界磁场下横向伊辛链自相关函数的长时间渐近性
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-20 DOI: 10.1007/s11005-026-02174-5
Noah Hout, Kenta Miyahara, Dustin Newland, Maxim Yattselev
{"title":"Long-time asymptotics of the autocorrelation function of the transverse Ising chain at the critical magnetic field revisited","authors":"Noah Hout,&nbsp;Kenta Miyahara,&nbsp;Dustin Newland,&nbsp;Maxim Yattselev","doi":"10.1007/s11005-026-02174-5","DOIUrl":"10.1007/s11005-026-02174-5","url":null,"abstract":"<div><p>Following [3], we analyze the long-time asymptotics of the autocorrelation function of the transverse Ising chain at the critical magnetic field (a special case of the spin-<span>(frac{1}{2})</span> XY model in a magnetic field) via the associated Riemann–Hilbert problem. We refine the original Deift–Zhou’s result by determining the subleading growing term in the asymptotics.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149234332","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
Marginally outer trapped surface with capillary boundary and rigidity of initial data sets 具有毛细边界和初始数据集刚性的边缘外捕获表面
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-17 DOI: 10.1007/s11005-026-02176-3
Sanghun Lee
{"title":"Marginally outer trapped surface with capillary boundary and rigidity of initial data sets","authors":"Sanghun Lee","doi":"10.1007/s11005-026-02176-3","DOIUrl":"10.1007/s11005-026-02176-3","url":null,"abstract":"<div><p>In this paper, we establish a series of rigidity results for initial data sets with boundary in the presence of marginally outer trapped surfaces (MOTSs) satisfying a capillary boundary condition. Our first result establishes area estimates for stable MOTS with capillary boundary. Building on this, we prove a rigidity theorem for three-dimensional initial data sets with boundary. We further extend the rigidity to higher dimensions by employing the Yamabe constant associated to the MOTS. Finally, under a low-index assumption, we obtain additional topological restrictions on MOTS with capillary boundary.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 6","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189622","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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