By Vincent Rivasseau (Chief Editor)

Articles during this volume:

1-17

On the Ultraviolet challenge for the second Weakly Interacting Fermi Gas

Giuseppe Benfatto

19-34

Borchers’ Commutation kin for Sectors with Braid team data in Low Dimensions

Jens Mund

35-60

Dispersion kinfolk within the Noncommutative three and Wess–Zumino version within the Yang–Feldman Formalism

Claus Döscher and Jochen Zahn

61-93

The impact of Time-Dependent Coupling on Non-Equilibrium regular States

Horia D. Cornean, Hagen Neidhardt and Valentin A. Zagrebnov

95-122

Sharp Asymptotics for the Neumann Laplacian with Variable Magnetic box: Case of size 2

Nicolas Raymond

123-143

Spectral and Scattering concept of Friedrichs types at the confident part Line with Hilbert–Schmidt Perturbations

Hellmut Baumgärtel

145-187

Mean-Field restrict and Semiclassical enlargement of a Quantum Particle System

Federica Pezzotti and Mario Pulvirenti

189-223

The hint formulation for Quantum Graphs with common Self Adjoint Boundary Conditions

Jens Bolte and Sebastian Endres

225-274

Dynamics of Bianchi kind I strategies of the Einstein Equations with Anisotropic Matter

Simone Calogero and J. Mark Heinzle

275-337

Convergent Null information Expansions at Space-Like Infinity of desk bound Vacuum Solutions

Andrés E. Aceña

339-356

Octonionic Twists for Supermembrane Matrix Models

Jens Hoppe, Douglas Lundholm and Maciej Trzetrzelewski

357-375

Unbounded Orbits for Semicircular Outer Billiard

Dmitry Dolgopyat and Bassam Fayad

377-394

On Confining Potentials and crucial Self-Adjointness for Schrödinger Operators on Bounded domain names in Rn

Gheorghe Nenciu and Irina Nenciu

395-414

A decrease certain at the First Spectral hole of Schrödinger Operators with Kato category Measures

Hendrik Vogt

415-428

High Frequency Dispersive Estimates in size Two

Simon Moulin

429-451

Entropy and rot of Correlations for actual Analytic Semi-Flows

Frédéric Naud

453-484

A Space-Time Characterization of the Kerr–Newman Metric

Willie W. Wong

485-511

Scaling restrict for Subsystems and Doplicher–Roberts Reconstruction

Roberto Conti and Gerardo Morsella

513-548

Bethe Ansatz for the common Weight Function

Luc Frappat, Sergey Khoroshkin, Stanislav Pakuliak and Éric Ragoucy

549-571

Scattering at 0 power for beautiful Homogeneous Potentials

Jan Dereziński and Erik Skibsted

573-575

A be aware on Low strength Scattering for Homogeneous Long-Range Potentials

Rupert L. Frank

577-621

Analytic Perturbation thought and Renormalization research of subject Coupled to Quantized Radiation

Marcel Griesemer and David G. Hasler

623-671

Regularity stipulations for Einstein’s Equations at Spatial Infinity

Juan Antonio Valiente Kroon

673-709

Multilinear Eigenfunction Estimates for the Harmonic Oscillator and the Nonlinear Schrödinger Equation with the Harmonic Potential

Takafumi Akahori and Kenichi Ito

711-747

Weyl legislation for partly Open Quantum Maps

Emmanuel Schenck

749-771

Analyticity for a few Operator capabilities from Statistical Quantum Mechanics

Kurt Hoke, Hans-Christoph Kaiser and Joachim Rehberg

773-792

Upper Estimates of the Density of States in a single measurement Interpolating among the Wegner and the Lifshitz Regime

Bernd Metzger

793-822

Operator Theoretic tools for the Eigenvalue Counting functionality in Spectral Gaps

Alexander Pushnitski

823-866

First Order method and Index Theorems for Discrete and Metric Graphs

Olaf Post

867-891

Tree Quantum box Theory

Razvan Gurau, Jacques Magnen and Vincent Rivasseau

893-912

Topological Censorship for Kaluza–Klein Space-Times

Piotr T. Chruściel, Gregory J. Galloway and Didier Solis

913-953

Physical nation for Nonrelativistic Quantum Electrodynamics

Fumio Hiroshima and Akito Suzuki

955-994

Supersymmetric Quantum box concept: Indefinite Metric

Florin Constantinescu

995-1025

Poisson and Diffusion Approximation of Stochastic grasp Equations with Control

Clément Pellegrini

1027-1073

Topological beneficial properties of huge Bosons on Two-Dimensional Einstein Space–Time

Romeo Brunetti, Lorenzo Franceschini and Valter Moretti

1075-1095

The internal Cauchy Horizon of Axisymmetric and desk bound Black Holes with Surrounding topic in Einstein–Maxwell idea: examine by way of Soliton Methods

Jörg Hennig and Marcus Ansorg

1097-1110

On the Spectrum of the Resonant Quantum Kicked Rotor

Italo Guarneri

1111-1139

Hecke Eigenfunctions of Quantized Cat Maps Modulo best Powers

Rikard Olofsson

1141-1158

A Galton–Watson Estimate for Dyson Series

Hans Maassen and Dmitri Botvich

1159-1205

On balance of Pseudo-Conformal Blowup for L2-critical Hartree NLS

Joachim Krieger, Enno Lenzmann and Pierre Raphaël

1207-1222

The floor nation of Relativistic Ions within the restrict of excessive Magnetic Fields

Doris H. Jakubassa-Amundsen

1223-1249

Dynamical section Transition for a Quantum Particle Source

Maximilian Butz and Herbert Spohn

1251-1284

Repeated and non-stop Interactions in Open Quantum Systems

Laurent Bruneau, Alain Joye and Marco Merkli

1285-1309

Gell-Mann and occasional formulation for Degenerate Unperturbed States

Christian Brouder, Gianluca Panati and Gabriel Stoltz

1311-1333

Non-Existence and strong point effects for Supercritical Semilinear Elliptic Equations

Jean Dolbeault and Robert Stańczy

1335-1358

Hilbert Lattice Equations

Norman D. Megill and Mladen Pavičić

1359-1376

Formation of Higher-dimensional Topological Black Holes

Filipe C. Mena, José Natário and Paul Tod

1377-1393

Perturbation process for Particle-like options of the Einstein–Dirac Equations

Simona Rota Nodari

1395-1417

On Heisenberg-like large team Structures

Ramon Peniche and O. A. Sánchez-Valenzuela

1419-1436

Invariant Tori in Hamiltonian platforms with excessive Order right Degeneracy

Yuecai Han, Yong Li and Yingfei Yi

1437-1486

A Gluing development concerning element debris typically Relativity

Iva Stavrov Allen

1487-1535

A building of continuous Scalar Curvature Manifolds with Delaunay-type Ends

Almir Silva Santos

1537-1557

All Vacuum close to Horizon Geometries in D-dimensions with (D − three) Commuting Rotational Symmetries

Stefan Hollands and Akihiro Ishibashi

1559-1604

The floor nation and the Long-Time Evolution within the CMC Einstein Flow

Martin Reiris

1605-1610

On traditional Superhomogeneous types for Minkowski Superspacetime

Ramon Peniche, G. Salgado and O. A. Sánchez-Valenzuela

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**Additional info for Annales Henri Poincaré - Volume 10**

**Sample text**

1. As suggested in [7], we do not subtract these terms (despite their naming), since they are neither local, nor, in general, divergent. We remark, however, that such a subtraction has been proposed in [25]. 2. The group velocity The sum of the zeroth order term (3) and the second order contribution (8) can be interpreted as the expansion (in λ) of 2π 0 ˆ d4 k fˆ(−k)h(k)θ(k )δ k 2 − m2 + λ2 Σ k 2 , (kσ)2 + O(λ4 ) . (11) This can be interpreted as a change of the dispersion relation. 2. This modiﬁcation of the dispersion relation is a manifestation of the breaking of particle Lorentz invariance, cf.

The Yukawa tadpole and the φ3 tadpole cancel (this has to be so in order to have a vanishing VEV of φ1 ). Using ˆ + (l) = 0 , (l2 − m2 )Δ ˆ A (l) = −(2π)−2 , (l2 − m2 )Δ the combination of the other terms gives Σ(k) = λ2 k 2 + m2 ˆ + (l)(1 + eikσl ) Δ ˆ R (k − l) + Δ ˆ R (k + l) . d4 l Δ Apart from the prefactor (k 2 +m2 ), this is exactly the expression we already found for the φ3 -model. We remark that for the self-energy of the fermion, one obtains the same result. Vol. 10 (2009) Dispersion Relations in Noncommutative Models 51 The prefactor is to be expected: Assuming that the non-renormalization the¯ θ2 θ¯2 -term gets renormalized.

The oscillatory integral for a can then be achieved if one calculates the limit n → ∞ after integrating, if this is well deﬁned and to a large extent independent of the choice of the sequence. 2. One could see the relation ds kdt l f (k)a(k, l)eiφ(k,l) = lim n→∞ ds kdt l f (k)gn (l)a(k, l)eiφ(k,l) (34) for a sequence gn of symbols with compact support and approaching 1, as a deﬁnition. The right hand side of (34), with ﬁnite n, is even deﬁned for a being some distribution. If the limit exists and is independent of the choice of the sequence gn out of some large class of sequences, this would be a reasonable extension.