Table Of ContentCRM Series in Mathematical Physics
Springer-Science+Business Media, LLC
CRM Series in Mathematical Physics
Conte, The Painleve Property: One Century Later
MacKenzie, Paranjape, and Zakrzewski, Solitons: Properties,
Dynamics, Interactions, Applications
Semenoff and Vinet, Particles and Fields
R. MacKenzie
M.B. Paranjape
WJ. Zakrzewski
Editors
Solitons
Properties, Dynamics,
Interactions, Applications
With 55 Figures
Springer
R. MacKenzie M.B. Paranjape W.J. Zakrzewski
Departement de physique Departement de physique Department of
Laboratoire Rene J. A. Levesque Laboratoire Rene J. A. Levesque Mathematical Sciences
Universite de Montreal Universite de Montreal Durham University
CP. 6128, succursale Centre-ville CP. 6128, succursale Centre-ville South Road
Montreal, Quebec H3C 3J7 Montreal, Quebec H3C 3J7 Durham DH1 3LE
Canada Canada UK
[email protected] [email protected] w ,j .zakrzewski @ durham. ac
Editorial Board
Joel S. Feldman Duong H. Phong
Department of Mathematics Department of Mathematics
University of British Columbia Columbia University
Vancouver, British Columbia V6T 1Z2 New York, NY 10027-0029
Canada USA
[email protected] [email protected]
Yvan Saint-Aubin Luc Vinet
Departement de mathematiques Department of Physics
Universite de Montreal McGill University
CP. 6128, succursale Centre-ville Rutherford Building
Montreal, Quebec H3C 3J7 Montreal, Quebec H3A 2T8
Canada Canada
[email protected] [email protected]
Library of Congress Cataloging-in-Publication Data
Solitons : properties, dynamics, interactions, applications
R. MacKenzie, M.B. Paranjape, W.J. Zakrzewski, [editors],
p. cm. - (The CRM series in mathematical physics)
Includes bibliographical references.
ISBN 978-1-4612-7063-8 ISBN 978-1-4612-1254-6 (eBook)
DOI 10.1007/978-1-4612-1254-6
1. Solitons Congresses. I. MacKenzie, R. (Richard)
II. Paranjape, M.B. III. Zakrzewski, W.J. IV. Series: CRM series
in mathematical physics.
QC174.26.W28S645 1999
530.12'4-dc21 99-16040
Printed on acid-free paper.
© 2000 Springer Science+Business Media New York
Originally published by Springer-Verlag New York, Inc. in 2000
Softcover reprint of the hardcover 1st edition 2000
All rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer-Science+Business Media, LLC),
except for brief excerpts in connection with reviews or scholarly analysis. Use
in connection with any form of information storage and retrieval, electronic adaptation, computer
software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the
former are not especially identified, is not to be taken as a sign that such names, as understood by
the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.
Production managed by Robert Bruni; manufacturing supervised by Jeffery Taub.
Photocomposed copy prepared from the authors' LaTeX files.
9 8 7 6 5 4 3 21
ISBN 978-1-4612-7063-8
Series Preface
The Centre de recherches mathematiques (CRM) was created in 1968 by
the Universite de Montreal to promote research in the mathematical sci
ences. Itis now a nationalinstitutethat hosts severalgroups, holds special
themeyears,summerschools,workshops,andapostdoctoralprogram.The
focus of its scientific activities ranges from pure to applied mathematics,
and includes statistics, theoretical computer science, mathematical meth
ods in biology and life sciences, and mathematical and theoretical physics.
The CRM also promotes collaboration between mathematicians and in
dustry. It is subsidized by the Natural Sciences and Engineering Research
Council ofCanada, the Fonds FCARofthe ProvinceofQuebec, the Cana
dianInstitutefor AdvancedResearchandhasprivateendowments. Current
activities, fellowships, and annual reports can be found on the CRM web
page at http://www.CRM.UMontreal.CAl.
The CRM Series in Mathematical Physics includes monographs, lecture
notes, and proceedings based on research pursued and events held at the
Centre de recherches mathematiques.
Yvan Saint-Aubin
Montreal
Preface
Solitons were discovered by John Scott Russel in 1834 and have interested
scientists and mathematicians ever since. They have been the subject ofa
largebodyofresearchinawidevarietyoffieldsofphysicsandmathematics,
not to mention engineering and other branches ofscience such as biology.
The workshop, "Solitons: Properties, Dynamics, Interactions, Applica
tions" was held at Queen's University, Kingston, Canada over the period
July 20-26, 1997. It was conceived as an interdisciplinary meeting wherein
top researchers from several of these fields could meet, interact, and ex
change ideas across traditional boundaries of research. During the work
shop,researchwaspresentedonmathematicalandnumericalaspectsofsoli
tons, as well as on applications ofsolitons to nuclear and particle physics,
cosmology, condensed matter physics, and to the recent developments in
string theory.
This volume consists of written versions of all talks presented at the
workshop. It isour hopethat peoplewithan interestinsolitonsinvirtually
anyfield ofresearch will find the range oftopics discussed both interesting
and inspiring.
R. MacKenzie
M.B. Paranjape
W.J. Zakrzewski
Contents
Series Preface v
Preface vii
List of Contributors xvii
1 Berry Phase and Dissipation ofTopological Singularities 1
Ping Ao and Xiao-Mei Zhu
1 Introduction.................... 1
2 Description ofthe Berry Phase and Dissipation 1
3 Effective Vortex Action 3
4 Discussion. 7
5 References........ 8
2 Normal Mode Spectra ofMulti-Skyrmions 11
W.K. Baskerville, C. Barnes, and N.G. Turok
1 Introduction............... 11
2 Method . . . . . . . . . . . . . . . . . 12
3 Results and Interpretation ofSpectra. 13
4 References................ 20
3 Standard-Model Dirac Particles Trapped in Flat
(Noncompact) Higher Dimensions 21
Ronald Bryan
1 Introduction.............. 21
2 Dirac Particle in Eight Flat Dimensions 22
3 References................. 24
4 Planar QED inMagneticorElectric Solitonic Backgrounds 27
Gerald Dunne
1 References........................... 30
5 Collective Coordinates and Inequivalent Coset Space
Quantizations 33
Juan Pedro Garrahan and Martin Kruczenski
1 References............................. 36
x Contents
6 Spatial Solitons ofthe Nonlinear Schrodinger Equation
ofArbitrary Nonlinearity with a Potential Hill 39
Boris V. Gisin
1 References.................... 43
0 • •
7 Hairs on the Unicorn: Fine Structure ofMonopoles
and Other Solitons 45
Alfred S. Goldhaber
1 Monopoles and Unicorns 45
0
1.1 Origin in medieval Europe . 46
1.2 Subject ofa vast literature 46
1.3 Never confirmed or captured 46
1.4 Unique unity, not usual duplexity . 46
1.5 Illuminates much about the world 46
1.6 Beautiful . . . . 46
0 • •
1.7 Poor cousins exist . . 47
1.8 Instantly recognizable 47
1.9 Still hope ofdiscovery 47
2 "Fundamental" and "Complementary" Solitons 47
3 Fractional and Peculiar Soliton Charges . . . . 49
4 Conditions for Integer F . . . . . 51
0 • • • • • • •
5 Questions About and Applications ofthe Jackiw-Rebbi
Monopole . 53
6 Conclusions 54
7 References. 54
8 A Model for Partially Polarized Quantum Hall States 57
ToH. Hansson and U. Nilsson
1 References ... 61
0 0 •••••• 0 •••••••••••• 0 •
9 Ordering Dynamics ofTopological Defect Networks 63
Mark Hindmarsh
1 References........... 66
0 • 0 • • • • 0 • • • 0 0 • •
10 Gauge Theory Description of Spin Chains and Ladders 69
Yutaka Hosotani
1 References........ 72
0 • • • • • • 0 • • • • • • • 0 • •
11 Soliton Solutions ofthe Integrable Chiral Model in
(2+1) Dimensions 75
Theodora Ioannidou
1 Introduction. 75
0 • 0 • • • • 0 0 • 0
2 Construction ofSoliton Solutions 76
3 References.... 79
0 • • • 0 • • 0 •
Contents xi
12 String Winding Modes From Charge Nonconservation
in Compact Chern-Simons Theory 81
Ian 1. Kogan
1 References 91
0 0 0 0 0 0 0 0 •• 0 • 0 0 0 0 •• 0 0 ••• 0 • 0
13 Holes in the Charge Density ofTopological Solitons 93
Mo Kugler
1 Introduction 93
0 0 0 0 • • •
2 The Existence ofHoles . 94
3 Discussion 96
0
4 References 96
0 0 0 0 0 0 • 0
14 From Two-dimensional Black Holes to sine-Gordon
Solitons 99
J Gegenberg and Go Kunstatter
0
1 Introduction 99
0 0 0 0 0 • 0 0 0 • • 0 0 0 0 0 0 0 0
2 Black Holes in Jackiw-Teitelboim Gravity 100
0 0
3 From Black Holes to sine-Gordon Solitons 103
0 • 0
4 . and Back Again 104
0 0
5 Speculations. 105
6 References 106
0 • 0 • • 0
15 Solitons and Exciton Superfluidity 107
1. Loutsenko and Do Roubtsov
1 References. 113
0 0 0 0 • 0 0 • 0 • 0 0 • 0
16 Quantum Effects on Higgs Winding Configurations 115
Arthur Lue
1 Introduction 115
0 0 0 ••• 0 0 • 0 0 • 0 0 0 0 0 0 •
2 Asymptotic Behavior ofthe Effective Action 116
0
3 Discussion 117
0
4 References 118
0 0 0 0 0 0 ••• 0 0 0 0 0 0
17 Solitons and Their Moduli Spaces 119
NoS. Manton
1 References.. 129
0 0 • 0 • 0 • • 0 0 0 0 0
18 Deformed Skyrmions 131
Lo Marleau
1 Introduction 131
0 0 0 0 0
2 The Static Oblate Soliton 131
3 Collective Variables . 132
4 Discussion 134
0
5 References. 134
0 0 0 0 0
xii Contents
19 The Large-N Renormalization Group 137
c
Nicholas Dorey and Michael P. Mattis
1 Introduction.............. 137
2 Large-N Hadron Models . 139
c
3 Summing the Leading-Order Graphs 140
4 Solving the Classical Field Equation 145
5 Large-N Renormalization Group 146
c
6 References............... 151
20 Instantons in Nonirreducible Representations ofthe
Lorentz Group 153
D.G.C. McKeon
1 References............................. 157
21 Fermion Vacuum Effects on Soliton Stability 159
Stephen G. Naculich
1 Nontopological Solitons ..... 159
2 Kinks in the Linear Sigma Model 160
3 References............. 162
22 Soliton Solutions ofthe u-Model and Disoriented
Chiral Condensates 163
Prasanta K. Panigrahi and C. Nagaraja Kumar
1 References................... 166
23 Dynamics ofTopological Magnetic Solitons 167
N. Papanicolaou
1 Introduction............ 167
2 Vorticity and Conservation Laws 168
3 Ferromagnets . . 172
4 Antiferromagnets 175
5 Superfluids 178
6 References.... 180
24 Fun with Baby-Skyrmions 183
T. Gisiger and M.B. Paranjape
1 Introduction.............. 183
2 Symmetries . . . . . . . . . . . . . . 183
3 Static and Spinning Baby-Skyrmions 184
4 The Model on 83 or R3 185
5 References............ 186
25 Skyrmions and Domain Walls 187
B.M.A.G. Piette and W.J. Zakrzewski
1 Introduction............. 187
