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Transforming Stäckel Hamiltonians of Benenti type to polynomial form 将Stäckel的Benenti型哈密顿变换为多项式形式
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2021-01-02 DOI: 10.4310/atmp.2022.v26.n3.a5
Jean de Dieu Maniraguha, K. Marciniak, C'elestin Kurujyibwami
{"title":"Transforming Stäckel Hamiltonians of Benenti type to polynomial form","authors":"Jean de Dieu Maniraguha, K. Marciniak, C'elestin Kurujyibwami","doi":"10.4310/atmp.2022.v26.n3.a5","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n3.a5","url":null,"abstract":"In this paper we discuss two canonical transformations that turn St\"{a}ckel separable Hamiltonians of Benenti type into polynomial form: transformation to Vi`ete coordinates and transformation to Newton coordinates. Transformation to Newton coordinates has been applied to these systems only very recently and in this paper we present a new proof that this transformation indeed leads to polynomial form of St\"{a}ckel Hamiltonians of Benenti type. Moreover we present all geometric ingredients of these Hamiltonians in both Vi`ete and Newton coordinates.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"32 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88381899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Advening to adynkrafields: Young tableaux to component fields of the 10D, $mathcal{N}=1$ scalar superfield 逼近标量超场:$mathcal{N}=1$标量超场，年轻的表格到10D的分量场
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2021-01-01 DOI: 10.4310/atmp.2021.v25.n6.a3
S. Gates, Yangrui Hu, S.-N. Hazel Mak
{"title":"Advening to adynkrafields: Young tableaux to component fields of the 10D, $mathcal{N}=1$ scalar superfield","authors":"S. Gates, Yangrui Hu, S.-N. Hazel Mak","doi":"10.4310/atmp.2021.v25.n6.a3","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n6.a3","url":null,"abstract":"","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"25 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81652124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 $mathcal{N}=2$ supersymmetric Calogero–Sutherland model and its eigenfunctions $mathcal{N}=2$超对称Calogero-Sutherland模型及其特征函数
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2021-01-01 DOI: 10.4310/atmp.2021.v25.n3.a1
L. Alarie-Vézina, L. Lapointe, P. Mathieu
{"title":"The $mathcal{N}=2$ supersymmetric Calogero–Sutherland model and its eigenfunctions","authors":"L. Alarie-Vézina, L. Lapointe, P. Mathieu","doi":"10.4310/atmp.2021.v25.n3.a1","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n3.a1","url":null,"abstract":"","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"32 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87018692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Calabi–Yau threefolds in $mathbb{P}^n$ and Gorenstein rings $mathbb{P}^n$和Gorenstein环中的Calabi-Yau三倍
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2020-11-21 DOI: 10.4310/atmp.2022.v26.n3.a7
H. Schenck, M. Stillman, Beihui Yuan
{"title":"Calabi–Yau threefolds in $mathbb{P}^n$ and Gorenstein rings","authors":"H. Schenck, M. Stillman, Beihui Yuan","doi":"10.4310/atmp.2022.v26.n3.a7","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n3.a7","url":null,"abstract":"A projectively normal Calabi-Yau threefold $X subseteq mathbb{P}^n$ has an ideal $I_X$ which is arithmetically Gorenstein, of Castelnuovo-Mumford regularity four. Such ideals have been intensively studied when $I_X$ is a complete intersection, as well as in the case where $X$ is codimension three. In the latter case, the Buchsbaum-Eisenbud theorem shows that $I_X$ is given by the Pfaffians of a skew-symmetric matrix. A number of recent papers study the situation when $I_X$ has codimension four. We prove there are 16 possible betti tables for an arithmetically Gorenstein ideal $I$ with $mathrm{codim}(I)=4=mathrm{reg}(I)$, and that exactly 8 of these occur for smooth irreducible nondegenerate threefolds. We investigate the situation in codimension five or more, obtaining examples of $X$ with $h^{p,q}(X)$ not among those appearing for $I_X$ of lower codimension or as complete intersections in toric Fano varieties. A key tool in our approach is the use of inverse systems to identify possible betti tables for $X$.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"106 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91286345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
The family of confluent Virasoro fusion kernels and a non-polynomial $q$-Askey scheme 收敛Virasoro融合核族和非多项式$q$-Askey格式
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2020-11-16 DOI: 10.4310/atmp.2021.v25.n6.a5
J. Lenells, J. Roussillon
{"title":"The family of confluent Virasoro fusion kernels and a non-polynomial $q$-Askey scheme","authors":"J. Lenells, J. Roussillon","doi":"10.4310/atmp.2021.v25.n6.a5","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n6.a5","url":null,"abstract":"We study the recently introduced family of confluent Virasoro fusion kernels $mathcal{C}_k(b,boldsymbol{theta},sigma_s,nu)$. We study their eigenfunction properties and show that they can be viewed as non-polynomial generalizations of both the continuous dual $q$-Hahn and the big $q$-Jacobi polynomials. More precisely, we prove that: (i) $mathcal{C}_k$ is a joint eigenfunction of four different difference operators for any positive integer $k$, (ii) $mathcal{C}_k$ degenerates to the continuous dual $q$-Hahn polynomials when $nu$ is suitably discretized, and (iii) $mathcal{C}_k$ degenerates to the big $q$-Jacobi polynomials when $sigma_s$ is suitably discretized. These observations lead us to propose the existence of a non-polynomial generalization of the $q$-Askey scheme. The top member of this non-polynomial scheme is the Virasoro fusion kernel (or, equivalently, Ruijsenaars' hypergeometric function), and its first confluence is given by the $mathcal{C}_k$.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"51 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86769731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Asymptotics of the Banana Feynman amplitudes at the large complex structure limit 大型复杂结构极限下香蕉费曼振幅的渐近性
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2020-11-11 DOI: 10.4310/ATMP.2022.v26.n5.a5
H. Iritani
{"title":"Asymptotics of the Banana Feynman amplitudes at the large complex structure limit","authors":"H. Iritani","doi":"10.4310/ATMP.2022.v26.n5.a5","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n5.a5","url":null,"abstract":"Recently Bonisch-Fischbach-Klemm-Nega-Safari discovered, via numerical computation, that the leading asymptotics of the l-loop Banana Feynman amplitude at the large complex structure limit can be described by the Gamma class of a degree (1,...,1) Fano hypersurface F in (P^1)^{l+1}. We confirm this observation by using a Gamma-conjecture type result for F.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"38 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90500969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Topological recursion for the extended Ooguri–Vafa partition function of colored HOMFLY-PT polynomials of torus knots 环面结的有色HOMFLY-PT多项式的扩展Ooguri-Vafa配分函数的拓扑递归
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2020-10-21 DOI: 10.4310/ATMP.2022.v26.n4.a1
P. Dunin-Barkowski, M. Kazarian, A. Popolitov, S. Shadrin, A. Sleptsov
{"title":"Topological recursion for the extended Ooguri–Vafa partition function of colored HOMFLY-PT polynomials of torus knots","authors":"P. Dunin-Barkowski, M. Kazarian, A. Popolitov, S. Shadrin, A. Sleptsov","doi":"10.4310/ATMP.2022.v26.n4.a1","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n4.a1","url":null,"abstract":"We prove that topological recursion applied to the spectral curve of colored HOMFLY-PT polynomials of torus knots reproduces the n-point functions of a particular partition function called the extended Ooguri-Vafa partition function. This generalizes and refines the results of Brini-Eynard-Marino and Borot-Eynard-Orantin. \u0000We also discuss how the statement of spectral curve topological recursion in this case fits into the program of Alexandrov-Chapuy-Eynard-Harnad of establishing the topological recursion for general weighted double Hurwitz numbers partition functions (a.k.a. KP tau-functions of hypergeometric type).","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"19 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74465737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 11
New structures in gravitational radiation 引力辐射的新结构
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2020-10-14 DOI: 10.4310/atmp.2022.v26.n3.a1
L. Bieri
{"title":"New structures in gravitational radiation","authors":"L. Bieri","doi":"10.4310/atmp.2022.v26.n3.a1","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n3.a1","url":null,"abstract":"We investigate the Einstein vacuum equations as well as the Einstein-null fluid equations describing neutrino radiation. We find new structures in gravitational waves and memory for asymptotically-flat spacetimes of slow decay. It has been known that for stronger decay of the data, including data being stationary outside a compact set, gravitational wave memory is finite and of electric parity only. In this article, we investigate general spacetimes that are asymptotically flat in a rough sense. That is, the decay of the data to Minkowski space towards infinity is very slow. As a main new feature, we prove that there exists diverging magnetic memory sourced by the magnetic part of the curvature tensor (a) in the Einstein vacuum and (b) in the Einstein-null-fluid equations. The magnetic memory occurs naturally in the Einstein vacuum setting (a) of pure gravity. In case (b), in the ultimate class of solutions, the magnetic memory contains also a curl term from the energy-momentum tensor for neutrinos also diverging at the aforementioned rate. The electric memory diverges too, it is generated by the electric part of the curvature tensor and in the Einstein-null-fluid situation also by the corresponding energy-momentum component. In addition, we find a panorama of finer structures in these manifolds. Some of these manifest themselves as additional contributions to both electric and magnetic memory. Our theorems hold for any type of matter or energy coupled to the Einstein equations as long as the data decays slowly towards infinity and other conditions are satisfied. The new results have a multitude of applications ranging from mathematical general relativity to gravitational wave astrophysics, detecting dark matter and other topics in physics.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"468 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86870009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Lorentz Meets Lipschitz 洛伦兹和利普希兹相遇
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2020-09-18 DOI: 10.4310/ATMP.2021.v25.n8.a4
Christian Lange, A. Lytchak, Clemens Samann
{"title":"Lorentz Meets Lipschitz","authors":"Christian Lange, A. Lytchak, Clemens Samann","doi":"10.4310/ATMP.2021.v25.n8.a4","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n8.a4","url":null,"abstract":"We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a $mathcal{C}^{1,1}$-parametrization and that they solve the geodesic equation in the sense of Filippov in this parametrization. Our proof shows that maximal causal curves are either everywhere lightlike or everywhere timelike. Furthermore, the proof demonstrates that maximal causal curves for an $alpha$-Holder continuous Lorentzian metric admit a $mathcal{C}^{1,frac{alpha}{4}}$-parametrization.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"13 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75800809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 9
Quasi-local mass near the singularity, the event horizon and the null infinity of black hole spacetimes 黑洞时空的奇点、视界和零无穷附近的准局部质量
IF 1.5 4区 物理与天体物理
Advances in Theoretical and Mathematical Physics Pub Date : 2020-09-10 DOI: 10.4310/ATMP.2021.v25.n1.a3
N. Gudapati, S. Yau
{"title":"Quasi-local mass near the singularity, the event horizon and the null infinity of black hole spacetimes","authors":"N. Gudapati, S. Yau","doi":"10.4310/ATMP.2021.v25.n1.a3","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n1.a3","url":null,"abstract":"The behaviour of geometric quantities close to geometric pathologies of a spacetime is relevant to deduce the physical behaviour of the system. In this work, we compute the quasi-local mass quantities - the Hawking mass, the Brown-York mass and the Liu-Yau mass in the maximal extensions of the spherically symmetric solutions of the Einstein equations inside the black hole region, at the singularity, the event horizon, and the null infinity, in the limiting sense of a geometric flow.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"53 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79841859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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