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Formules de Feynmann-Kac pour le modèle de Nelson ultra-violet renormalisée 重整化Nelson紫外模型的Feynmann-Kac公式
IF 1.1 4区 数学 Q1 MATHEMATICS Pub Date : 2017-01-10 DOI: 10.24033/ast.1054
O. Matte, J. S. Møller
We derive Feynman-Kac formulas for the ultra-violet renormalized Nelson Hamiltonian with a Kato decomposable external potential and for corresponding fiber Hamiltonians in the translation invariant case. We simultaneously treat massive and massless bosons. Furthermore, we present a non-perturbative construction of a renormalized Nelson Hamiltonian in the non-Fock representation defined as the generator of a corresponding Feynman-Kac semi-group. Our novel analysis of the vacuum expectation of the Feynman-Kac integrands shows that, if the external potential and the Pauli-principle are dropped, then the spectrum of the $N$-particle renormalized Nelson Hamiltonian is bounded from below by some negative universal constant times $g^4N^3$, for all values of the coupling constant $g$. A variational argument also yields an upper bound of the same form for large $g^2N$. We further verify that the semi-groups generated by the ultra-violet renormalized Nelson Hamiltonian and its non-Fock version are positivity improving with respect to a natural self-dual cone, if the Pauli principle is ignored. In another application we discuss continuity properties of elements in the range of the semi-group of the renormalized Nelson Hamiltonian.
我们导出了具有加托可分解外势的紫外重整化纳尔逊哈密顿量的费曼-卡茨公式以及平移不变情况下相应的纤维哈密顿量的费曼-卡茨公式。我们同时处理有质量和无质量玻色子。进一步,我们给出了非fock表示中的重规格化Nelson hamilton算子的非摄动构造,该构造被定义为相应的Feynman-Kac半群的生成器。我们对Feynman-Kac积分的真空期望的新分析表明,如果放弃外势和保利原理,那么对于所有耦合常数g$, N$粒子重归一化的纳尔逊哈密顿量的谱从下面被一个负的通用常数乘以g^4N^3$所限制。对于较大的$g^2N$,变分参数也给出了相同形式的上界。在忽略泡利原理的情况下,我们进一步验证了由紫外重正化Nelson hamilton算子及其非fock算子生成的半群对于自然自对偶锥是正改进的。在另一个应用中,我们讨论了重归一化纳尔逊哈密顿算子半群范围内元素的连续性。
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引用次数: 20
A C^1 Arnol'd-Liouville theorem C^1阿诺-刘维尔定理
IF 1.1 4区 数学 Q1 MATHEMATICS Pub Date : 2016-12-23 DOI: 10.24033/ast.1109
M. Arnaud, Jinxin Xue
In this paper, we prove a version of Arnol'd-Liouville theorem for C 1 commuting Hamiltonians. We show that the Lipschitz regularity of the foliation by invariant Lagrangian tori is crucial to determine the Dynamics on each Lagrangian torus and that the C 1 regularity of the foliation by invariant Lagrangian tori is crucial to prove the continuity of Arnol'd-Liouville coordinates. We also explore various notions of C 0 and Lipschitz integrability.
在本文中,我们证明了c1可交换哈密顿量的Arnol'd-Liouville定理的一个版本。我们证明了不变拉格朗日环面叶化的Lipschitz正则性对于确定每个拉格朗日环面上的动力学是至关重要的,而不变拉格朗日环面叶化的c1正则性对于证明Arnol'd-Liouville坐标的连续性是至关重要的。我们还探讨了c0和Lipschitz可积性的各种概念。
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引用次数: 6
Tilting modules and the p-canonical basis 倾斜模与p-正则基
IF 1.1 4区 数学 Q1 MATHEMATICS Pub Date : 2015-12-28 DOI: 10.24033/ast.1041
S. Riche, G. Williamson
In this paper we propose a new approach to tilting modules for reductive algebraic groups in positive characteristic. We conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on the principal block. Our conjecture implies character formulas for the simple and tilting modules in terms of the p-canonical basis, as well as a description of the principal block as the anti-spherical quotient of the Hecke category. We prove our conjecture for GL_n using the theory of 2-Kac-Moody actions. Finally, we prove that the diagrammatic Hecke category of a general crystallographic Coxeter group may be described in terms of parity complexes on the flag variety of the corresponding Kac-Moody group.
本文提出了一种求正特征代数群的可倾模的新方法。我们推测平移函子给出仿射Weyl群的(图解)Hecke范畴在主块上的作用。我们的猜想包含了用p-正则基表示的简单和倾斜模的特征公式,以及作为Hecke范畴的反球商的主块的描述。我们用2-Kac-Moody作用理论证明了GL_n的猜想。最后,我们证明了一般晶体学Coxeter群的图解Hecke范畴可以用相应的Kac-Moody群的旗变体上的宇称配合物来描述。
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引用次数: 131
AST418 - A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean case 酉群的Gan-Gross-Prasad猜想的一个局部迹公式:阿基米德情况
IF 1.1 4区 数学 Q1 MATHEMATICS Pub Date : 2015-06-04 DOI: 10.24033/ast.1120
Raphael Beuzart-Plessis
In this paper, we prove, following earlier work of Waldspurger ([Wa1], [Wa4]), a sort of local relative trace formula which is related to the local Gan-Gross-Prasad conjecture for unitary groups over a local field $F$ of characteristic zero. As a consequence, we obtain a geometric formula for certain multiplicities $m(pi)$ appearing in this conjecture and deduce from it a weak form of the local Gan-Gross-Prasad conjecture (multiplicity one in tempered L-packets). These results were already known over $p$-adic fields and thus are only new when $F=mathbb{R}$.
本文继Waldspurger ([Wa1], [Wa4])的早期工作之后,证明了特征为零的局部域$F$上的酉群的一类与局部Gan-Gross-Prasad猜想有关的局部相对迹公式。因此,我们得到了该猜想中出现的某些多重性$m(pi)$的几何公式,并由此推导出局部Gan-Gross-Prasad猜想的弱形式(调和l包中的多重性1)。这些结果在$p$-adic字段中是已知的,因此只有当$F=mathbb{R}$时才是新的。
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引用次数: 17
The Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane 仿射平面多项式自同态的动力学模型-朗猜想
IF 1.1 4区 数学 Q1 MATHEMATICS Pub Date : 2015-03-02 DOI: 10.24033/ast.1038
Junyi Xie
In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane.
本文证明了仿射平面上多项式自同态的动力学莫德尔-朗猜想。
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引用次数: 24
Periods and harmonic analysis on spherical varieties 球形品种的周期和谐波分析
IF 1.1 4区 数学 Q1 MATHEMATICS Pub Date : 2012-02-29 DOI: 10.24033/ast.1040
Y. Sakellaridis, Akshay Venkatesh
Given a spherical variety X for a group G over a non-archimedean local field k, the Plancherel decomposition for L^2(X) should be related to "distinguished" Arthur parameters into a dual group closely related to that defined by Gaitsgory and Nadler. Motivated by this, we develop, under some assumptions on the spherical variety, a Plancherel formula for L^2(X) up to discrete (modulo center) spectra of its "boundary degenerations", certain G-varieties with more symmetries which model X at infinity. Along the way, we discuss the asymptotic theory of subrepresentations of C^{infty}(X), and establish conjectures of Ichino-Ikeda and Lapid-Mao. We finally discuss global analogues of our local conjectures, concerning the period integrals of automorphic forms over spherical subgroups.
给定群G在非阿基米德局部域k上的球形变化X, L^2(X)的Plancherel分解应与将Arthur参数“区分”为与Gaitsgory和Nadler定义的对偶群密切相关有关。在此基础上,我们在对球变分的一些假设下,建立了L^2(X)直至其“边界退化”的离散(模中心)谱的Plancherel公式。最后,我们讨论了关于球面子群上自同构形式的周期积分的局部猜想的全局类似。
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引用次数: 194
Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions] 粗糙系数常微分方程与Ambrosio的重整化定理[源自Ambrosio, DiPerna, Lions]
IF 1.1 4区 数学 Q1 MATHEMATICS Pub Date : 2008-01-01 DOI: 10.5167/UZH-21441
Camillo De Lellis
In a seminal paper of almost 20 years ago, R.J. DiPerna and P.-L. Lions initiated the theory of renormalized solutions to study the well-posedness of Ordinary Differential Equations and Transport Equations with discontinuous coefficients. In a recent work L. Ambrosio solved the long-standing open problem of extending this theory to BV coefficients, the most common functional-analytic closure of classical functions with jump discontinuities. Besides its intrinsic interest, Ambrosio's Theorem has been used to solve relevant problems in Partial Differential Equations and it opened the way to a series of new questions.
在近20年前的一篇开创性论文中,R.J.迪珀纳和p.l。狮子开创了重整化解理论,以研究具有不连续系数的常微分方程和输运方程的适定性。在最近的工作中,L. Ambrosio解决了将该理论扩展到BV系数的长期开放问题,BV系数是具有跳跃不连续的经典函数的最常见的泛函解析闭包。安布罗西奥定理除了其固有的兴趣外,还被用于解决偏微分方程中的相关问题,并为一系列新问题开辟了道路。
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引用次数: 12
H[∞]functional calculus and square functions on noncommutative L[p]-spaces 非交换L[p]-空间上的H[∞]泛函微积分与平方函数
IF 1.1 4区 数学 Q1 MATHEMATICS Pub Date : 2006-12-01 DOI: 10.24033/AST.698
M. Junge, C. Merdy, Quanhua Xu
— We investigate sectorial operators and semigroups acting on noncommutative L-spaces. We introduce new square functions in this context and study their connection with H∞ functional calculus, extending some famous work by Cowling, Doust, McIntoch and Yagi concerning commutative L-spaces. This requires natural variants of Rademacher sectoriality and the use of the matricial structure of noncommutative L-spaces. We mainly focus on noncommutative diffusion semigroups, that is, semigroups (Tt)t≥0 of normal selfadjoint operators on a semifinite von Neumann algebra (M, τ) such that Tt : Lp(M) → Lp(M) is a contraction for any p ≥ 1 and any t ≥ 0. We discuss several examples of such semigroups for which we establish bounded H∞ functional calculus and square function estimates. This includes semigroups generated by certain Hamiltonians or Schur multipliers, q-Ornstein-Uhlenbeck semigroups acting on the q-deformed von Neumann algebras of Bozejko-Speicher, and the noncommutative Poisson semigroup acting on the group von Neumann algebra of a free group. c © Astérisque 305, SMF 2006
研究了作用于非交换l空间上的扇区算子和半群。在此背景下,我们引入了新的平方函数,并研究了它们与H∞泛函微积分的联系,推广了Cowling、Doust、McIntoch和Yagi关于可交换l空间的一些著名工作。这需要Rademacher扇形的自然变异体和非交换l空间的材料结构的使用。我们主要研究半有限von Neumann代数(M, τ)上的正规自伴随算子的非交换扩散半群(Tt)t≥0,使得Tt: Lp(M)→Lp(M)是任意p≥1和任意t≥0的收缩。我们讨论了这类半群的几个例子,并建立了有界H∞泛函演算和平方函数估计。这包括由某些hamilton或Schur乘子生成的半群,作用于bozejco - speicher的q-变形冯·诺伊曼代数上的q-Ornstein-Uhlenbeck半群,以及作用于自由群的群冯·诺伊曼代数上的非交换泊松半群。c©ast risque 305, SMF 2006
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引用次数: 94
Quantum integrable systems 量子可积系统
IF 1.1 4区 数学 Q1 MATHEMATICS Pub Date : 1994-01-01 DOI: 10.1090/cbms/125/11
M. Semenov-Tian-Shansky
© Société mathématique de France, 1995, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
©法国数学学会,1995,版权所有。访问收藏“星号”(http://smf4.emath.fr/ Publications/Asterisque/)的档案意味着同意一般使用条件(http://www.numdam.org/conditions)。任何有系统的商业使用或印刷都是刑事犯罪。本文件的任何副本或打印必须包含此版权声明。
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引用次数: 1
Minimal K-types for GLn over a p-adic field p进域上GLn的最小k型
IF 1.1 4区 数学 Q1 MATHEMATICS Pub Date : 1988-01-01 DOI: 10.2307/2000877
R. Howe, A. Moy
© Société mathématique de France, 1989, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
©法国数学学会,1989,保留所有权利。访问收藏“星号”(http://smf4.emath.fr/ Publications/Asterisque/)的档案意味着同意一般使用条件(http://www.numdam.org/conditions)。任何有系统的商业使用或印刷都是刑事犯罪。本文件的任何副本或打印必须包含此版权声明。
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引用次数: 21
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Asterisque
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