Annales Henri Poincaré最新文献

Integrable Multi-Hamiltonian Systems from Reduction of an Extended Quasi-Poisson Double of ({text {U}}(n)) 的扩展拟泊松二重的可积多哈密顿系统的约化 ({text {U}}(n))

IF 1.5 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2023-07-06 DOI: 10.1007/s00023-023-01344-8

M. Fairon, L. Fehér

{"title":"Integrable Multi-Hamiltonian Systems from Reduction of an Extended Quasi-Poisson Double of ({text {U}}(n))","authors":"M. Fairon, L. Fehér","doi":"10.1007/s00023-023-01344-8","DOIUrl":"10.1007/s00023-023-01344-8","url":null,"abstract":"<div><p>We construct a master dynamical system on a <span>({text {U}}(n))</span> quasi-Poisson manifold, <span>({mathcal {M}}_d)</span>, built from the double <span>({text {U}}(n) times {text {U}}(n))</span> and <span>(dge 2)</span> open balls in <span>(mathbb {C}^n)</span>, whose quasi-Poisson structures are obtained from <span>(T^* mathbb {R}^n)</span> by exponentiation. A pencil of quasi-Poisson bivectors <span>(P_{underline{z}})</span> is defined on <span>({mathcal {M}}_d)</span> that depends on <span>(d(d-1)/2)</span> arbitrary real parameters and gives rise to pairwise compatible Poisson brackets on the <span>({text {U}}(n))</span>-invariant functions. The master system on <span>({mathcal {M}}_d)</span> is a quasi-Poisson analogue of the degenerate integrable system of free motion on the extended cotangent bundle <span>(T^*!{text {U}}(n) times mathbb {C}^{ntimes d})</span>. Its commuting Hamiltonians are pullbacks of the class functions on one of the <span>({text {U}}(n))</span> factors. We prove that the master system descends to a degenerate integrable system on a dense open subset of the smooth component of the quotient space <span>({mathcal {M}}_d/{text {U}}(n))</span> associated with the principal orbit type. Any reduced Hamiltonian arising from a class function generates the same flow via any of the compatible Poisson structures stemming from the bivectors <span>(P_{underline{z}})</span>. The restrictions of the reduced system on minimal symplectic leaves parameterized by generic elements of the center of <span>({text {U}}(n))</span> provide a new real form of the complex, trigonometric spin Ruijsenaars–Schneider model of Krichever and Zabrodin. This generalizes the derivation of the compactified trigonometric RS model found previously in the <span>(d=1)</span> case.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"24 10","pages":"3461 - 3529"},"PeriodicalIF":1.5,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01344-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"6713726","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: 1

Morawetz Estimates Without Relative Degeneration and Exponential Decay on Schwarzschild–de Sitter Spacetimes 史瓦西-德西特时空上无相对退化和指数衰减的Morawetz估计

IF 1.5 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2023-06-20 DOI: 10.1007/s00023-023-01293-2

Georgios Mavrogiannis

{"title":"Morawetz Estimates Without Relative Degeneration and Exponential Decay on Schwarzschild–de Sitter Spacetimes","authors":"Georgios Mavrogiannis","doi":"10.1007/s00023-023-01293-2","DOIUrl":"10.1007/s00023-023-01293-2","url":null,"abstract":"<div><p>We use a novel physical space method to prove <i>relatively</i> non-degenerate integrated energy estimates for the wave equation on subextremal Schwarzschild–de?Sitter spacetimes with parameters <span>((M,Lambda ))</span>. These are integrated decay statements whose bulk energy density, though degenerate at highest order, is everywhere comparable to the energy density of the boundary fluxes. As a corollary, we prove that solutions of the wave equation decay exponentially on the exterior region. The main ingredients are a previous Morawetz estimate of Dafermos–Rodnianski and an additional argument based on commutation with a vector field which can be expressed in the form </p><div><div><span>$$begin{aligned} rsqrt{1-frac{2M}{r}-frac{Lambda }{3}r^2}frac{partial }{partial r}, end{aligned}$$</span></div></div><p>where <span>(partial _r)</span> here denotes the coordinate vector field corresponding to a well-chosen system of hyperboloidal coordinates. Our argument gives exponential decay also for small first-order perturbations of the wave operator. In the limit <span>(Lambda =0)</span>, our commutation corresponds to the one introduced by Holzegel–Kauffman (A note on the wave equation on black hole spacetimes with small non-decaying first-order terms, 2020. arXiv:2005.13644).</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"24 9","pages":"3113 - 3152"},"PeriodicalIF":1.5,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01293-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4800279","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: 5

Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model 三维量子引力的跃迁振幅:彩色布拉托夫模型中的边界和全息

IF 1.5 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2023-06-14 DOI: 10.1007/s00023-023-01330-0

Christophe Goeller, Daniele Oriti, Gabriel Schmid

引用次数: 0

({hat{Z}})-Invariant for SO(3) and OSp(1|2) Groups ({hat{Z}})- SO(3)和OSp(1|2)群的不变性

IF 1.5 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2023-06-06 DOI: 10.1007/s00023-023-01332-y

Sachin Chauhan, Pichai Ramadevi

引用次数: 1

Price’s Law and Precise Late-Time Asymptotics for Subextremal Reissner–Nordström Black Holes 次极值Reissner-Nordström黑洞的Price定律和精确晚时渐近性

IF 1.5 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2023-06-02 DOI: 10.1007/s00023-023-01328-8

Yannis Angelopoulos, Stefanos Aretakis, Dejan Gajic

引用次数: 12

The Quantization of Proca Fields on Globally Hyperbolic Spacetimes: Hadamard States and Møller Operators 全局双曲时空上Proca场的量子化:Hadamard态和Møller算子

IF 1.5 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2023-05-29 DOI: 10.1007/s00023-023-01326-w

Valter Moretti, Simone Murro, Daniele Volpe

{"title":"The Quantization of Proca Fields on Globally Hyperbolic Spacetimes: Hadamard States and Møller Operators","authors":"Valter Moretti, Simone Murro, Daniele Volpe","doi":"10.1007/s00023-023-01326-w","DOIUrl":"10.1007/s00023-023-01326-w","url":null,"abstract":"<div><p>This paper deals with several issues concerning the algebraic quantization of the real Proca field in a globally hyperbolic spacetime and the definition and existence of Hadamard states for that field. In particular, extending previous work, we construct the so-called M?ller <span>(*)</span>-isomorphism between the algebras of Proca observables on paracausally related spacetimes, proving that the pullback of these isomorphisms preserves the Hadamard property of corresponding quasifree states defined on the two spacetimes. Then, we pull back a natural Hadamard state constructed on ultrastatic spacetimes of bounded geometry, along this <span>(*)</span>-isomorphism, to obtain an Hadamard state on a general globally hyperbolic spacetime. We conclude the paper, by comparing the definition of an Hadamard state, here given in terms of wavefront set, with the one proposed by Fewster and Pfenning, which makes use of a supplementary Klein–Gordon Hadamard form. We establish an (almost) complete equivalence of the two definitions.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"24 9","pages":"3055 - 3111"},"PeriodicalIF":1.5,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01326-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5130187","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: 1

Quand Galilée et Carroll engendrent Lorentz 当伽利略和卡罗尔生下洛伦兹时

IF 1.5 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2023-05-14 DOI: 10.1007/s00023-023-01321-1

Jean-Marc Lévy-Leblond

引用次数: 1

Cosmological de Sitter Solutions of the Semiclassical Einstein Equation 半经典爱因斯坦方程的宇宙学德西特解

IF 1.5 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2023-05-09 DOI: 10.1007/s00023-023-01315-z

Hanno Gottschalk, Nicolai R. Rothe, Daniel Siemssen

{"title":"Cosmological de Sitter Solutions of the Semiclassical Einstein Equation","authors":"Hanno Gottschalk, Nicolai R. Rothe, Daniel Siemssen","doi":"10.1007/s00023-023-01315-z","DOIUrl":"10.1007/s00023-023-01315-z","url":null,"abstract":"<div><p>Exponentially expanding space–times play a central role in contemporary cosmology, most importantly in the theory of inflation and in the dark energy driven expansion in the late universe. In this work, we give a complete list of de Sitter solutions of the semiclassical Einstein equation (SCE), where classical gravity is coupled to the expected value of a renormalized stress–energy tensor of a free quantum field in the Bunch–Davies state. To achieve this, we explicitly determine the stress–energy tensor associated with the Bunch–Davies state using the recently proposed “moment approach” on the cosmological coordinate patch of de Sitter space. From the energy component of the SCE, we thus obtain an analytic consistency equation for the model’s parameters which has to be fulfilled by solutions to the SCE. Using this equation, we then investigate the number of solutions and the structure of the solution set in dependency on the coupling parameter of the quantum field to the scalar curvature and renormalization constants using analytic arguments in combination with numerical evidence. We also identify parameter sets where multiple expansion rates separated by several orders of magnitude are possible. Potentially for such parameter settings, a fast (semi-stable) expansion in the early universe could be compatible with a late-time “Dark Energy-like” behavior of the universe.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"24 9","pages":"2949 - 3029"},"PeriodicalIF":1.5,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01315-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4394112","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: 3

On the Mass Dependence of the Modular Operator for a Double Cone 双锥模算子的质量依赖性

IF 1.5 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2023-05-04 DOI: 10.1007/s00023-023-01311-3

Henning Bostelmann, Daniela Cadamuro, Christoph Minz

引用次数: 5

Anisotropic Spin Generalization of Elliptic Macdonald–Ruijsenaars Operators and R-Matrix Identities 椭圆型Macdonald-Ruijsenaars算子和r -矩阵恒等式的各向异性自旋推广

IF 1.5 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2023-05-03 DOI: 10.1007/s00023-023-01316-y

M. Matushko, Andrei Zotov

引用次数: 9