Geometric methods in physics : XXXIV Workshop, Białowieża, Poland, June 28-July 4, 2015 PDF
Preview Geometric methods in physics : XXXIV Workshop, Białowieża, Poland, June 28-July 4, 2015
Trends in Mathematics Piotr Kielanowski S. Twareque Ali Pierre Bieliavsky Anatol Odzijewicz Martin Schlichenmaier Theodore Voronov Editors Geometric Methods in Physics (cid:59)(cid:59)(cid:59)(cid:44)(cid:57)(cid:3)(cid:58)(cid:82)(cid:85)(cid:78)(cid:86)(cid:75)(cid:82)(cid:83)(cid:15)(cid:3)(cid:37)(cid:76)(cid:68)(cid:242)(cid:82)(cid:90)(cid:76)(cid:72)(cid:365)a, Poland, June 28 – July 4, 2015 Trends in Mathematics Trends in Mathematics is a series devoted to the publication of volumes arising from conferences and lecture series focusing on a particular topic from any area of mathematics. Its aim is to make current developments available to the community as rapidly as possible without compromise to quality and to archive these for reference. Proposals for volumes can be submitted using the Online Book Project Submission Form at our website www.birkhauser-science.com. Material submitted for publication must be screened and prepared as follows: All contributions should undergo a reviewing process similar to that carried out by journals and be checked for correct use of language which, as a rule, is English. Articles without proofs, or which do not contain any significantly new results, should be rejected. High quality survey papers, however, are welcome. We expect the organizers to deliver manuscripts in a form that is essentially ready for direct reproduction. Any version of TEX is acceptable, but the entire collection of files must be in one particular dialect of TEX and unified according to simple instructions available from Birkhäuser. Furthermore, in order to guarantee the timely appearance of the proceedings it is essential that the final version of the entire material be submitted no later than one year after the conference. Moreinformationaboutthisseriesathttp://www.springer.com/series/4961 Geometric Methods in Physics Piotr Kielanowski • S. Twareque Ali • Pierre Bieliavsky Anatol Odzijewicz • Martin Schlichenmaier Theodore Voronov Editors XXXIV Workshop, Bia(cid:225)owie(cid:298)a, Poland, June 28 – July 4, 2015 Editors Piotr Kielanowski S. Twareque Ali Departamento de Física Department of Mathematics and Statistics CINVESTAV Concordia University Mexico City, Distrito Federal, Mexico Montreal, Québec, Canada Pierre Bieliavsky Anatol Odzijewicz Department de Mathematiques Institute of Mathematics Université Catholique de Louvain University of Bia(cid:225)ystok Louvain-la-Neuve, Belgium Bia(cid:225)ystok, Poland Martin Schlichenmaier Theodore Voronov Mathematics Research Unit, FSTC School of Mathematics University of Luxembourg University of Manchester Luxembourg-Kirchberg, Luxembourg Manchester, United Kingdom ISSN 2297-0215 ISSN 2297-024 X (electronic) TrendsinMathematics ISBN 978-3-319-31755-7 ISBN 978-3-319-31756-4 (eBook) DOI 10.1007/978-3-319-31756-4 Library of Congress Control Number: 2016942575 Mathematics Subject Classification (2010): 01-06, 01A70, 20N99, 58A50, 58Z05, 81P16 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser. The registered company is Springer International Publishing AG Switzerland (www.birkhauser-science.com) Contents In Memoriam S. Twareque Ali (1942–2016) ............................... ix Preface .................................................................. xi Part I: Quantum Structures: G´erard Emch in memoriam T. Ali G´erardG. Emch .................................................... 3 A. Emch-D´eriaz The G´erardI knew for Sixty Years! ................................. 5 F. Bagarello Pseudo-bosons and Riesz Bi-coherent States ......................... 15 I. Fujimoto Entropy of Completely Positive Maps and Applications to Quantum Information Theory ....................................... 25 G.A. Goldin Some Comments on Indistinguishable Particles and Interpretation of the Quantum Mechanical Wave Function ......................... 35 G.L. Sewell Hyperbolic Flows and the Question of Quantum Chaos .............. 45 A. Chattopadhyay and K.B. Sinha A New Proof of the Helton–Howe–Carey–PincusTrace Formula ..... 57 T. Kanazawa and A. Yoshioka Quasi-classical Calculation of Eigenvalues: Examples and Questions ............................................ 69 vi Contents Part II: Representation Theory and Harmonic Analysis A. Alldridge Supergroup Actions and Harmonic Analysis ......................... 81 I. Belti¸ta˘ and D. Belti¸ta˘ Representations of Nilpotent Lie Groups via Measurable Dynamical Systems ................................................. 95 G. Dhont and B.I. Zhilinsk´ı Symbolic Interpretation of the Molien Function: Free and Non-free Modules of Covariants ..................................... 105 B. Janssens and K.-H. Neeb Momentum Maps for Smooth Projective Unitary Representations ..................................................... 115 V.F. Molchanov Canonical Representations for Hyperboloids: an Interaction with an Overalgebra ............................................... 129 Yu.A. Neretin On p-adic Colligations and ‘Rational Maps’ of Bruhat–Tits Trees .... 139 J. Hilgert, A. Pasquale and T. Przebinda Resonances for the Laplacian: the Cases BC and C 2 2 (except SO (p,2) with p>2 odd) ................................... 159 0 T. Przebinda Howe’s Correspondence and Characters ............................. 183 Part III: Quantum Mechanics and Integrable Systems A.V. Domrin Local Inverse Scattering ............................................ 193 D.J. Ferna´ndez C. Painlev´e Equations and Supersymmetric Quantum mechanics ....... 213 T. Iwai and B. Zhilinskii Change in Energy Eigenvalues Against Parameters .................. 233 H. Kuwabara, T. Yumibayashi and H. Harada Time-dependent Pais–Uhlenbeck Oscillator and Its Decomposition ...................................................... 255 Contents vii T. Tate Quantum Walks in Low Dimension .................................. 261 Part IV: Algebraic Structures M.N. Hounkonnou and M.L. Dassoundo Center-symmetric Algebras and Bialgebras: Relevant Properties and Consequences .................................................. 281 M. Schlichenmaier N-point Virasoro Algebras Considered as Krichever–Novikov Type Algebras ...................................................... 295 Part V: Field Theory and Quantization A. Deser Star Products on Graded Manifolds and α(cid:2)-corrections to Double Field Theory ............................................. 311 A. Sergeev Adiabatic Limit in Ginzburg–Landauand Seiberg–Witten Equations ........................................................... 321 A.A. Sharapov Variational Tricomplex and BRST Theory .......................... 331 S. Wu Quantization of Hitchin’s Moduli Space of a Non-orientable Surface ............................................................. 343 Part VI: Complex Geometry Z. Pasternak-Winiarski and P.M. W´ojcicki Ramadanov Theorem for Weighted Bergman Kernels on Complex Manifolds ................................................. 367 Z. Pasternak-Winiarski and P.M. W´ojcicki A Characterizationof Domains of Holomorphy by Means of Their Weighted Skwarczyn´ski Distance .............................. 375 Part VII: Special Talk by Bogdan Mielnik B. Mielnik Science and its Constraints (an unfinished story) .................... 387 P M G W V ski) (cid:276) XI oli X G X sz e ma h o s of t o by T nt ot a h p P ci ( rti a P In Memoriam S. Twareque Ali (1942–2016) As this volume went to press, we were saddened to learn of the sudden passing of our good friend and colleague, S. Twareque Ali. As a member of the Organizing Committee of the Workshopon Geometric Methods in Physics, and a participant eachsummerfor25years,Twarequegaveselflesslyofhistimeandenergytoensure thesuccessoftheseries.Hewillbelongrememberedforhisscientificachievements, his generosity of spirit, and his devoted leadership.
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