Geometric Methods in Physics: XXXIV Workshop, Bialowieża, Poland, June 28 - July 4, 2015

393 Pages·2016·9.913 MB·English

by  Piotr Kielanowski, S. Twareque Ali, Pierre Bieliavsky, Anatol Odzijewicz, Martin Schlichenmaier, Theodore Voronov

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

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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
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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
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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.