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A note on Huisken’s isoperimetric mass 关于惠斯肯等周质量的说明
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-21 DOI: 10.1007/s11005-024-01883-z
Jeffrey L. Jauregui, Dan A. Lee, Ryan Unger
{"title":"A note on Huisken’s isoperimetric mass","authors":"Jeffrey L. Jauregui,&nbsp;Dan A. Lee,&nbsp;Ryan Unger","doi":"10.1007/s11005-024-01883-z","DOIUrl":"10.1007/s11005-024-01883-z","url":null,"abstract":"<div><p>In this short note, we explain that Huisken’s isoperimetric mass is always nonnegative for elementary reasons.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679860","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
Two homomorphisms from the affine Yangian associated with (widehat{mathfrak {sl}}(n)) to the affine Yangian associated with (widehat{mathfrak {sl}}(n+1)) 从与(widehat{mathfrak {sl}}(n)) 相关的仿射杨格到与(widehat{mathfrak {sl}}(n+1)) 相关的仿射杨格的两个同态关系
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-14 DOI: 10.1007/s11005-024-01879-9
Mamoru Ueda
{"title":"Two homomorphisms from the affine Yangian associated with (widehat{mathfrak {sl}}(n)) to the affine Yangian associated with (widehat{mathfrak {sl}}(n+1))","authors":"Mamoru Ueda","doi":"10.1007/s11005-024-01879-9","DOIUrl":"10.1007/s11005-024-01879-9","url":null,"abstract":"<div><p>We construct a homomorphism from the affine Yangian <span>(Y_{hbar ,varepsilon +hbar }(widehat{mathfrak {sl}}(n)))</span> to the affine Yangian <span>(Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n+1)))</span> which is different from the one in Ueda (A homomorphism from the affine Yangian <span>(Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n)))</span> to the affine Yangian <span>(Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n+1)))</span>, 2023. arXiv:2312.09933). By using this homomorphism, we give a homomorphism from <span>(Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n))otimes Y_{hbar ,varepsilon +nhbar }(widehat{mathfrak {sl}}(m)))</span> to <span>(Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(m+n)))</span>. As an application, we construct a homomorphism from the affine Yangian <span>(Y_{hbar ,varepsilon +nhbar }(widehat{mathfrak {sl}}(m)))</span> to the centralizer algebra of the pair of affine Lie algebras <span>((widehat{mathfrak {gl}}(m+n),widehat{mathfrak {sl}}(n)))</span> and the coset vertex algebra of the pair of rectangular <i>W</i>-algebras <span>(mathcal {W}^k(mathfrak {gl}(2m+2n),(2^{m+n})))</span> and <span>(mathcal {W}^{k+m}(mathfrak {sl}(2n),(2^{n})))</span>.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636842","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
Ground states of fermionic nonlinear Schrödinger systems with Coulomb potential I: the (L^2)-subcritical case 具有库仑势的费米子非线性薛定谔系统的基态 I：(L^2)-次临界情况
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-14 DOI: 10.1007/s11005-024-01877-x
Bin Chen, Yujin Guo
{"title":"Ground states of fermionic nonlinear Schrödinger systems with Coulomb potential I: the (L^2)-subcritical case","authors":"Bin Chen,&nbsp;Yujin Guo","doi":"10.1007/s11005-024-01877-x","DOIUrl":"10.1007/s11005-024-01877-x","url":null,"abstract":"<div><p>We consider ground states of the <i>N</i> coupled fermionic nonlinear Schrödinger systems with the Coulomb potential <i>V</i>(<i>x</i>) in the <span>(L^2)</span>-subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter <span>(alpha &gt;0)</span>, which represents the attractive strength of the non-relativistic quantum particles. The limiting behavior of ground states for the system is also analyzed as <span>(alpha rightarrow infty )</span>, where the mass concentrates at one of the singular points for the Coulomb potential <i>V</i>(<i>x</i>).\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636846","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
Quantum intersection numbers and the Gromov–Witten invariants of ({{{mathbb {C}}}{{mathbb {P}}}}^1) 量子交集数和（{{mathbb {C}}}{{mathbb {P}}}}^1) ）的格罗莫夫-维滕不变式
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-13 DOI: 10.1007/s11005-024-01869-x
Xavier Blot, Alexandr Buryak
{"title":"Quantum intersection numbers and the Gromov–Witten invariants of ({{{mathbb {C}}}{{mathbb {P}}}}^1)","authors":"Xavier Blot,&nbsp;Alexandr Buryak","doi":"10.1007/s11005-024-01869-x","DOIUrl":"10.1007/s11005-024-01869-x","url":null,"abstract":"<div><p>The notion of a quantum tau-function for a natural quantization of the KdV hierarchy was introduced in a work of Dubrovin, Guéré, Rossi, and the second author. A certain natural choice of a quantum tau-function was then described by the first author, the coefficients of the logarithm of this series are called the quantum intersection numbers. Because of the Kontsevich–Witten theorem, a part of the quantum intersection numbers coincides with the classical intersection numbers of psi-classes on the moduli spaces of stable algebraic curves. In this paper, we relate the quantum intersection numbers to the stationary relative Gromov–Witten invariants of <span>(({{{mathbb {C}}}{{mathbb {P}}}}^1,0,infty ))</span> with an insertion of a Hodge class. Using the Okounkov–Pandharipande approach to such invariants (with the trivial Hodge class) through the infinite wedge formalism, we then give a short proof of an explicit formula for the “purely quantum” part of the quantum intersection numbers, found by the first author, which in particular relates these numbers to the one-part double Hurwitz numbers.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636891","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
Fermionic integrable models and graded Borchers triples 费米子可积分模型和梯度博尔赫斯三元组
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-06 DOI: 10.1007/s11005-024-01865-1
Henning Bostelmann, Daniela Cadamuro
{"title":"Fermionic integrable models and graded Borchers triples","authors":"Henning Bostelmann,&nbsp;Daniela Cadamuro","doi":"10.1007/s11005-024-01865-1","DOIUrl":"10.1007/s11005-024-01865-1","url":null,"abstract":"<div><p>We provide an operator-algebraic construction of integrable models of quantum field theory on 1+1-dimensional Minkowski space with fermionic scattering states. These are obtained by a grading of the wedge-local fields or, alternatively, of the underlying Borchers triple defining the theory. This leads to a net of graded-local field algebras, of which the even part can be considered observable, although it is lacking Haag duality. Importantly, the nuclearity condition implying nontriviality of the local field algebras is independent of the grading, so that existing results on this technical question can be utilized. Application of Haag–Ruelle scattering theory confirms that the asymptotic particles are indeed fermionic. We also discuss connections with the form factor programme.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01865-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587877","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
Weakly periodic p-adic quasi-Gibbs measures for the Potts model on a Cayley tree Cayley 树上 Potts 模型的弱周期 p-adic 准吉布斯量度
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-05 DOI: 10.1007/s11005-024-01872-2
Muzaffar Rahmatullaev, Akbarkhuja Tukhtabaev, Nurkhon Samijonova
{"title":"Weakly periodic p-adic quasi-Gibbs measures for the Potts model on a Cayley tree","authors":"Muzaffar Rahmatullaev,&nbsp;Akbarkhuja Tukhtabaev,&nbsp;Nurkhon Samijonova","doi":"10.1007/s11005-024-01872-2","DOIUrl":"10.1007/s11005-024-01872-2","url":null,"abstract":"<div><p>In the present paper, we study the weakly periodic <i>p</i>-adic quasi-Gibbs measures for the three-state Potts model on a Cayley tree of order two. Under some conditions, we show there exist 14 weakly periodic (non-periodic) <i>p</i>-adic quasi-Gibbs measures. Moreover, if <span>(p=3)</span> then there are six weakly periodic <i>p</i>-adic Gibbs measures for this model. We also prove that if <span>(pne 3)</span> then a phase transition occurs for the Potts model on a Cayley tree of order two.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579449","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
Twisting factors and fixed-time models in quantum field theory 量子场论中的扭曲因子和固定时间模型
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-04 DOI: 10.1007/s11005-024-01878-w
Ezio Vasselli
{"title":"Twisting factors and fixed-time models in quantum field theory","authors":"Ezio Vasselli","doi":"10.1007/s11005-024-01878-w","DOIUrl":"10.1007/s11005-024-01878-w","url":null,"abstract":"<div><p>We construct a class of fixed-time models in which the commutations relations of a Dirac field with a bosonic field are non-trivial and depend on the choice of a given distribution (“twisting factor”). If the twisting factor is fundamental solution of a differential operator, then applying the differential operator to the bosonic field yields a generator of the local gauge transformations of the Dirac field. Charged vectors generated by the Dirac field define states of the bosonic field which in general are not local excitations of the given reference state. The Hamiltonian density of the bosonic field presents a non-trivial interaction term: besides creating and annihilating bosons, it acts on momenta of fermionic wave functions. When the twisting factor is the Coulomb potential, the bosonic field contributes to the divergence of an electric field and its Laplacian generates local gauge transformations of the Dirac field. In this way, we get a fixed-time model fulfilling the equal time commutation relations of the interacting Coulomb gauge.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579423","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
Nonexistence of closed and bounded null geodesics in Kerr spacetimes 克尔空间中封闭有界空大地线的不存在性
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-04 DOI: 10.1007/s11005-024-01875-z
Giulio Sanzeni
{"title":"Nonexistence of closed and bounded null geodesics in Kerr spacetimes","authors":"Giulio Sanzeni","doi":"10.1007/s11005-024-01875-z","DOIUrl":"10.1007/s11005-024-01875-z","url":null,"abstract":"<div><p>The Kerr-star spacetime is the extension over the horizons and in the negative radial region of the slowly rotating Kerr black hole. It is known that below the inner horizon, there exist both timelike and null (lightlike) closed curves. Nevertheless, we prove that null geodesics can be neither closed nor even contained in a compact subset of the Kerr-star spacetime.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579442","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
General covariance for quantum states over time 量子态随时间变化的一般协方差
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-11-01 DOI: 10.1007/s11005-024-01870-4
James Fullwood
{"title":"General covariance for quantum states over time","authors":"James Fullwood","doi":"10.1007/s11005-024-01870-4","DOIUrl":"10.1007/s11005-024-01870-4","url":null,"abstract":"<div><p>Quantum states over time are a spatiotemporal generalization of density operators which were first introduced to give a more even-handed treatment of space and time in quantum theory. In particular, quantum states over time encode not only spatial, but also <i>causal</i> correlations associated with the dynamical evolution of a quantum system, and the association of quantum states over time with the dynamical flow of quantum information is in direct analogy with spacetime and its relation to classical dynamics. In this work, we further such an analogy by formulating a notion of general covariance for the theory of quantum states over time. We then associate a canonical state over time with a density operator which is to evolve under a sequence of quantum processes modeled by completely positive trace-preserving (CPTP) maps, and we show that such a canonical state over time satisfies such a notion of covariance. We also show that the dynamical quantum Bayes’ rule transforms covariantly with respect to quantum states over time, and we conclude with a discussion of what it means for a physical law to be generally covariant when formulated in terms of quantum states over time.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142565752","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
Combinatorial 2d higher topological quantum field theory from a local cyclic (A_infty ) algebra 从局部循环（A_infty ）代数出发的组合 2d 高等拓扑量子场论
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-10-30 DOI: 10.1007/s11005-024-01874-0
Justin Beck, Andrey Losev, Pavel Mnev
{"title":"Combinatorial 2d higher topological quantum field theory from a local cyclic (A_infty ) algebra","authors":"Justin Beck,&nbsp;Andrey Losev,&nbsp;Pavel Mnev","doi":"10.1007/s11005-024-01874-0","DOIUrl":"10.1007/s11005-024-01874-0","url":null,"abstract":"<div><p>We construct combinatorial analogs of 2d higher topological quantum field theories. We consider triangulations as vertices of a certain CW complex <span>(Xi )</span>. In the “flip theory,” cells of <span>(Xi _textrm{flip})</span> correspond to polygonal decompositions obtained by erasing the edges in a triangulation. These theories assign to a cobordism <span>(Sigma )</span> a cochain <i>Z</i> on <span>(Xi _textrm{flip})</span> constructed as a contraction of structure tensors of a cyclic <span>(A_infty )</span> algebra <i>V</i> assigned to polygons. The cyclic <span>(A_infty )</span> equations imply the closedness equation <span>((delta +Q)Z=0)</span>. In this context, we define combinatorial BV operators and give examples with coefficients in <span>(mathbb {Z}_2)</span>. In the “secondary polytope theory,” <span>(Xi _textrm{sp})</span> is the secondary polytope (due to Gelfand–Kapranov–Zelevinsky) and the cyclic <span>(A_infty )</span> algebra has to be replaced by an appropriate refinement that we call an <span>(widehat{A}_infty )</span> algebra. We conjecture the existence of a good Pachner CW complex <span>(Xi )</span> for any cobordism, whose local combinatorics is described by secondary polytopes and the homotopy type is that of Zwiebach’s moduli space of complex structures. Depending on this conjecture, one has an “ideal model” of combinatorial 2d HTQFT determined by a local <span>(widehat{A}_infty )</span> algebra.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01874-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555275","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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