By Vincent Rivasseau (Chief Editor)

Articles during this volume:

1-17

On the Ultraviolet challenge for the 2nd Weakly Interacting Fermi Gas

Giuseppe Benfatto

19-34

Borchers’ Commutation family for Sectors with Braid team information in Low Dimensions

Jens Mund

35-60

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

Claus Döscher and Jochen Zahn

61-93

The impression 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 variety I strategies of the Einstein Equations with Anisotropic Matter

Simone Calogero and J. Mark Heinzle

275-337

Convergent Null info 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 sure at the First Spectral hole of Schrödinger Operators with Kato classification 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 strength for beautiful Homogeneous Potentials

Jan Dereziński and Erik Skibsted

573-575

A observe on Low power Scattering for Homogeneous Long-Range Potentials

Rupert L. Frank

577-621

Analytic Perturbation idea and Renormalization research of topic 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 in part 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 procedure 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 kingdom for Nonrelativistic Quantum Electrodynamics

Fumio Hiroshima and Akito Suzuki

955-994

Supersymmetric Quantum box conception: Indefinite Metric

Florin Constantinescu

995-1025

Poisson and Diffusion Approximation of Stochastic grasp Equations with Control

Clément Pellegrini

1027-1073

Topological positive factors of big 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 subject in Einstein–Maxwell thought: learn 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 country of Relativistic Ions within the restrict of excessive Magnetic Fields

Doris H. Jakubassa-Amundsen

1223-1249

Dynamical part 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 area of expertise 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 approach for Particle-like ideas of the Einstein–Dirac Equations

Simona Rota Nodari

1395-1417

On Heisenberg-like large workforce Structures

Ramon Peniche and O. A. Sánchez-Valenzuela

1419-1436

Invariant Tori in Hamiltonian structures with excessive Order right Degeneracy

Yuecai Han, Yong Li and Yingfei Yi

1437-1486

A Gluing development relating to aspect debris generally Relativity

Iva Stavrov Allen

1487-1535

A development of continuing 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 flooring nation and the Long-Time Evolution within the CMC Einstein Flow

Martin Reiris

1605-1610

On normal Superhomogeneous versions for Minkowski Superspacetime

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

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**Example text**

Grosse and R. Wulkenhaar, Renormalisation of φ4 -theory on non-commutative R4 to all orders, Lett. Math. Phys. 71 (2005), 13, [arXiv:hep-th/0403232]. [22] P. Heslop and K. Sibold, Quantized equations of motion in non-commutative theories, Eur. Phys. J. C 41 (2005), 545, [arXiv:hep-th/0411161]. [23] E. Langmann and R. J. Szabo, Duality in scalar ﬁeld theory on noncommutative phase spaces, Phys. Lett. B 533 (2002), 168, [arXiv:hep-th/0202039]. Vol. 10 (2009) Dispersion Relations in Noncommutative Models 59 [24] Y.

But there are some changes for the currents. It is an interesting feature of noncommutative interacting theories that the local9 currents associated to symmetries are in general not conserved [16, 42]. Examples are the energy-momentum tensor in the φ4 -model [27] and in electrodynamics [18]. , for λ = 0. We discuss this in terms of the superﬁeld Φ. The equation of motion is 1 ¯2 ¯ Φ + mΦ + λΦΦ = 0 . − D 4 The local supercurrent is given by Vαα˙ = 1 ¯ + i{∂/αα˙ Φ, Φ} ¯ . ¯ α˙ Φ] ¯ − i{Φ, ∂/αα˙ Φ} [Dα Φ, D 2 Here we used a symmetrized version of the usual current, since this is usually advantageous in the noncommutative case.

Longo, Modular structure and duality in conformal ﬁeld theory, Commun. Math. Phys. 156 (1993), 201–219. [11] D. Buchholz and K. Fredenhagen, Locality and the structure of particle states, Commun. Math. Phys 84 (1982), 1–54. [12] A. Connes, The Tomita–Takesaki theory and classiﬁcation of type-III factors, Proc. Int. School Phys. Enrico Fermi, 1973, pp. 29–46. [13] S. Doplicher, R. Haag, and J. E. Roberts, Local observables and particle statistics I, Commun. Math. Phys. 23 (1971), 199. [14] S. Doplicher, R.