Related papers: Integrability, Seiberg-Witten Models and Picard-Fu…

This is a version of the author's diploma thesis written at the University of Cologne in 2002/03. The topic is the construction of Seiberg-Witten invariants of closed 3-manifolds. In analogy to the four dimensional case, the structure of…

Errors and paradoxes in quantum mechanics, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear

We make corrections on the paper by Sugino [{\it JHEP} {\bf 0501} (2005) 016].

This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of…

Translation of 'Die Logik Nicht Gleichzeitig Entscheidbarer Aussagen' by Ernst Specker, Dialectica, vol. 14, 239 - 246 (1960).

This is the foreword to the book we edited on the origins and early development of supersymmetry, which has been just issued by World Scientific. This book presents a view on the discovery of supersymmetry and pioneering investigations…

An outline of J\"org Eschmeier's main mathematical contributions is organized both on a historical perspective, as well as on a few distinct topics. The reader can grasp from our essay the dynamics of spectral theory of commutative tuples…

These lectures are devoted to the low energy limit of \N2 SUSY gauge theories, which is described in terms of integrable systems. A special emphasis is on a duality that naturally acts on these integrable systems. The duality turns out to…

Contents: 1 Frustrated quantum spin systems 1.1 The Pyrochlore checkerboard 1.2 Singlets in reflection symmetric spin systems 2 Wehrl entropy of Bloch coherent states 2.1 Conjectures of Wehrl and Lieb 2.2 Proof of Lieb's conjecture for low…

This is a survey article concerning applications of Hilbert's metric in the analysis and dynamics of linear and nonlinear mappings on cones. It will appear as a chapter in the "Handbook of Hilbert geometry", ed. G. Besson, A. Papadopoulos…

Article for the forthcoming Encyclopedia of Mathematical Physics, to be published by Elsevier. Covers kinks & breathers, sigma-models & Skyrmions, abelian-Higgs vortices, monopoles, Yang-Mills instantons, and Q-balls.

This is the introduction I wrote for the multi-authored book "From Riemann to differential geometry and relativity", edited by L. Ji, A. Papadopoulos and S. Yamada (Berlin, Springer verlag, 2017). The book consists of twenty chapters,…

Forty-six years after the birth of supersymmetry in 1973 from works of Julius Wess and Bruno Zumino, the standard quantum-field-theorists and particle physicists' language of `superspaces', `supersymmetry', and `supersymmetric action…

We compare the results of our two papers with the results of the paper Aratyn H., Gomes J.F., Zimerman A.H., Higher order Painlev\'e equations and their symmetries via reductions of a class of integrable models, J. Phys. A: Math. Theor., V.…

A discussion on the contribution of Peshkov, Bertin, Ginelli and Chate, arxiv:1404.3275v1, in this special issue.

Contents (Part 1): 1.Derivation of Lorentz Invariance and Three Space Dimensions in Generic Field Theory (C D. Froggatt and H. B. Nielsen) 2.Unitary Representations, Noncompact Groups SO(q; d - q)...(N. Mankoc Borstnik, H. B. Nielsen and D.…

This survey contains an exposition of ideas and results related to Faltings' proof of the conjectures of Shafarevich, Tate and Mordell. This paper originally appeared in 1986 as an Appendix to the Russian translation of Serge Lang,…

This is the 8th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. The article reviews the superconformal index. It is often simpler to calculate than instanton partition functions,…

We discuss additional supersymmetries for N = (2, 2) supersymmetric non-linear sigma models described by left and right semichiral superfields.

These supplementary notes in the ArXiv are a companion to our paper "Bocher contractions of conformally superintegrable Laplace equations" [arXiv:1512.09315]. They contain background material and the details of the extensive computations…