Annales Henri Poincaré - Volume 10 by Vincent Rivasseau (Chief Editor)

By Vincent Rivasseau (Chief Editor)

Articles during this volume:

On the Ultraviolet challenge for the second Weakly Interacting Fermi Gas
Giuseppe Benfatto

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

Dispersion kinfolk within the Noncommutative three and Wess–Zumino version within the Yang–Feldman Formalism
Claus Döscher and Jochen Zahn

The impact of Time-Dependent Coupling on Non-Equilibrium regular States
Horia D. Cornean, Hagen Neidhardt and Valentin A. Zagrebnov

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

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

Mean-Field restrict and Semiclassical enlargement of a Quantum Particle System
Federica Pezzotti and Mario Pulvirenti

The hint formulation for Quantum Graphs with common Self Adjoint Boundary Conditions
Jens Bolte and Sebastian Endres

Dynamics of Bianchi kind I strategies of the Einstein Equations with Anisotropic Matter
Simone Calogero and J. Mark Heinzle

Convergent Null information Expansions at Space-Like Infinity of desk bound Vacuum Solutions
Andrés E. Aceña

Octonionic Twists for Supermembrane Matrix Models
Jens Hoppe, Douglas Lundholm and Maciej Trzetrzelewski

Unbounded Orbits for Semicircular Outer Billiard
Dmitry Dolgopyat and Bassam Fayad

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

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

High Frequency Dispersive Estimates in size Two
Simon Moulin

Entropy and rot of Correlations for actual Analytic Semi-Flows
Frédéric Naud

A Space-Time Characterization of the Kerr–Newman Metric
Willie W. Wong

Scaling restrict for Subsystems and Doplicher–Roberts Reconstruction
Roberto Conti and Gerardo Morsella

Bethe Ansatz for the common Weight Function
Luc Frappat, Sergey Khoroshkin, Stanislav Pakuliak and Éric Ragoucy

Scattering at 0 power for beautiful Homogeneous Potentials
Jan Dereziński and Erik Skibsted

A be aware on Low strength Scattering for Homogeneous Long-Range Potentials
Rupert L. Frank

Analytic Perturbation thought and Renormalization research of subject Coupled to Quantized Radiation
Marcel Griesemer and David G. Hasler

Regularity stipulations for Einstein’s Equations at Spatial Infinity
Juan Antonio Valiente Kroon

Multilinear Eigenfunction Estimates for the Harmonic Oscillator and the Nonlinear Schrödinger Equation with the Harmonic Potential
Takafumi Akahori and Kenichi Ito

Weyl legislation for partly Open Quantum Maps
Emmanuel Schenck

Analyticity for a few Operator capabilities from Statistical Quantum Mechanics
Kurt Hoke, Hans-Christoph Kaiser and Joachim Rehberg

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

Operator Theoretic tools for the Eigenvalue Counting functionality in Spectral Gaps
Alexander Pushnitski

First Order method and Index Theorems for Discrete and Metric Graphs
Olaf Post

Tree Quantum box Theory
Razvan Gurau, Jacques Magnen and Vincent Rivasseau

Topological Censorship for Kaluza–Klein Space-Times
Piotr T. Chruściel, Gregory J. Galloway and Didier Solis

Physical nation for Nonrelativistic Quantum Electrodynamics
Fumio Hiroshima and Akito Suzuki

Supersymmetric Quantum box concept: Indefinite Metric
Florin Constantinescu

Poisson and Diffusion Approximation of Stochastic grasp Equations with Control
Clément Pellegrini

Topological beneficial properties of huge Bosons on Two-Dimensional Einstein Space–Time
Romeo Brunetti, Lorenzo Franceschini and Valter Moretti

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

On the Spectrum of the Resonant Quantum Kicked Rotor
Italo Guarneri

Hecke Eigenfunctions of Quantized Cat Maps Modulo best Powers
Rikard Olofsson

A Galton–Watson Estimate for Dyson Series
Hans Maassen and Dmitri Botvich

On balance of Pseudo-Conformal Blowup for L2-critical Hartree NLS
Joachim Krieger, Enno Lenzmann and Pierre Raphaël

The floor nation of Relativistic Ions within the restrict of excessive Magnetic Fields
Doris H. Jakubassa-Amundsen

Dynamical section Transition for a Quantum Particle Source
Maximilian Butz and Herbert Spohn

Repeated and non-stop Interactions in Open Quantum Systems
Laurent Bruneau, Alain Joye and Marco Merkli

Gell-Mann and occasional formulation for Degenerate Unperturbed States
Christian Brouder, Gianluca Panati and Gabriel Stoltz

Non-Existence and strong point effects for Supercritical Semilinear Elliptic Equations
Jean Dolbeault and Robert Stańczy

Hilbert Lattice Equations
Norman D. Megill and Mladen Pavičić

Formation of Higher-dimensional Topological Black Holes
Filipe C. Mena, José Natário and Paul Tod

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

On Heisenberg-like large team Structures
Ramon Peniche and O. A. Sánchez-Valenzuela

Invariant Tori in Hamiltonian platforms with excessive Order right Degeneracy
Yuecai Han, Yong Li and Yingfei Yi

A Gluing development concerning element debris typically Relativity
Iva Stavrov Allen

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

All Vacuum close to Horizon Geometries in D-dimensions with (D − three) Commuting Rotational Symmetries
Stefan Hollands and Akihiro Ishibashi

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

On traditional Superhomogeneous types for Minkowski Superspacetime
Ramon Peniche, G. Salgado and O. A. Sánchez-Valenzuela

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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.

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