Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA is a refereed electronic journal for publication of papers in the following areas:

  • Geometrical methods in mathematical physics
  • Lie theory and differential equations
  • Classical and quantum integrable systems
  • Dynamical systems and chaos
  • Exactly and quasi-exactly solvable models
  • Lie groups and algebras, representation theory
  • Orthogonal polynomials and special functions
  • Quantum algebras, quantum groups and noncommutative geometry
  • Supersymmetry and supergravity, strings and branes
  • Cosmology and quantum gravity


Editor: Anatoly Nikitin (Institute of Mathematics, Kyiv (Kiev), Ukraine)

Associate Editors: Vyacheslav Boyko, Roman Popovych, Iryna Yehorchenko, Alexander Zhalij

Executive Assistant: Vira Pobyzh

SIGMA is owned, operated and funded by researchers of the Department of Applied Research, Institute of Mathematics of National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka Street, Kyiv 4, 01601 Ukraine

Editorial Board

Mark Ablowitz (University of Colorado, USA)
Mark Adler (Brandeis University, USA)
Alexander Andrianov (Saint Petersburg State University, Russia)
Paolo Aschieri (E. Fermi Centre, Rome and University Piemonte Orientale, Alessandria, Italy)
Glenn Barnich (Université Libre de Bruxelles, Belgium)
Martin Bojowald (Pennsylvania State University, USA)
Richard Borcherds (University of California, Berkeley, USA)
Francesco Calogero (University of Rome "La Sapienza", Italy)
James Carlson (Clay Mathematics Institute and University of Utah, USA)
Peter Clarkson (University of Kent at Canterbury, UK)
Edward Corrigan (University of York, UK)
Thomas Curtright (University of Miami, USA)
Robbert Dijkgraaf (University of Amsterdam, The Netherlands and Institute for Advanced Study, Princeton, USA)
Boris Dubrovin (International School for Advanced Studies (SISSA), Trieste, Italy)
Charles Dunkl (University of Virginia, USA)
Michael Eastwood (Australian National University, Canberra, Australia)
László Fehér (Research Institute for Particle and Nuclear Physics, Budapest and University of Szeged, Hungary)
Athanassios Fokas (University of Cambridge, UK)
Allan Fordy (University of Leeds, UK)
Stavros Garoufalidis (Georgia Institute of Technology, Atlanta, USA)
Basile Grammaticos (Université Paris VII, France)
Harald Grosse (University of Vienna, Austria)
Rod Gover (University of Auckland, New Zealand)
Darryl D. Holm (Imperial College London, UK)
Johannes Huebschmann (Université des Sciences et Technologies de Lille, France)
Jacques Hurtubise (McGill University, Montreal, Canada)
Niky Kamran (McGill University, Montreal, Canada)
Boris Khesin (University of Toronto, Canada)
Evgueni Khruslov (Verkin Institute for Low Temperature Physics, Kharkiv, Ukraine)
Anatol Kirillov (Kyoto University, Japan)
Erik Koelink (Radboud University Nijmegen, The Netherlands)
Tom Koornwinder (University of Amsterdam, The Netherlands)
Yvette Kosmann-Schwarzbach (École Polytechnique, France)
Alan Kostelecky (Indiana University, USA)
Dirk Kreimer (Humboldt-Universität zu Berlin, Germany)
Igor Krichever (Columbia University, USA)
Petr Kulish (Petersburg Department of Steklov Institute of Mathematics, St.Petersburg, Russia)
Giovanni Landi (University of Trieste, Italy)
Eugene Lerman (University of Illinois at Urbana-Champaign, USA)
Jerzy Lukierski (University of Wroclaw, Poland)
Kirill C.H. Mackenzie (University of Sheffield, UK)
Robert Mann (University of Waterloo, Canada)
Alexander Mikhailov (University of Leeds, UK)
Willard Miller, Jr. (University of Minnesota, Minneapolis, USA)
Robert Minlos (Institute for Information Transmission Problems, Moscow, Russia)
Robert Moody (University of Victoria, Victoria, Canada)
Mikhail Olshanetsky (Institute of Theoretical and Experimental Physics, Moscow, Russia)
Grigori Olshanski (Institute for Information Transmission Problems, Moscow, Russia)
Peter Olver (University of Minnesota, Minneapolis, USA)
Jiri Patera (Centre de Recherches Mathematiques, Montreal, Canada)
Orlando Ragnisco (Universita di Roma 3, Italy)
Pierre Ramond (University of Florida, USA)
Tudor Ratiu (Ecole Polytechnique Fédérale de Lausanne, Switzerland)
Carlo Rovelli (Centre de Physique Theorique de Luminy, Marseille, France)
Simon Ruijsenaars (University of Leeds and Loughborough University, UK)
Vadim Schechtman (Université Paul Sabatier, Toulouse, France)
Israel Michael Sigal (University of Toronto, Canada)
Andrei Smilga (Universite de Nantes, France)
Daniel Sternheimer (Universite de Bourgogne, Dijon, France and Keio University, Yokohama, Japan)
Jasper Stokman (University of Amsterdam, The Netherlands)
Yuri Suris (Technische Universität Berlin, Germany)
Richard Szabo (Heriot-Watt University, Edinburgh, UK)
Kanehisa Takasaki (Kyoto University, Japan)
Arkady Tseytlin (Imperial College London, UK and Lebedev Institute, Moscow, Russia)
Alexander Varchenko (University of North Carolina at Chapel Hill, USA)
Erik Verlinde (University of Amsterdam, The Netherlands)
Pavel Winternitz (Centre de Recherches Mathematiques, Montreal, Canada)

Authors who wish to have their manuscript handled by a specific member of the Editorial Board should notify the Editorial Office (about this) at the time of submission.

How to Submit an Article

Please submit the paper to and send the arXive number to or (only in exceptional cases) you can send the zipped paper in TeX/LaTeX format directly to (please include the PDF or PostScript file as well) with explanation why you prefer not to put the paper to arXiv.

Your article may be prepared for submission in any TeX-style of your choice. Though we would like to point out that after the paper is accepted for publication you should prepare the paper in accordance to the SIGMA style (which can be downloaded from here).

Please indicate in your submission if your paper is intended for a specific special issue of SIGMA.

If you do not receive a confirmation within two working days that we have received your paper, please resend it to our alternative address

The length of an article is not limited.

We are accepting only two submissions per author, per year.

The average time of the paper processing (from the submission of the paper to its appearance on the journal's web site) is 2–4 months. However, this essentially depends on the subject and the length of the article, so in some cases the processing can take longer.

The papers are considered for publication if they have not been published previously and are not submitted for publication elsewhere.

SIGMA is an open access journal. Nevertheless, despite open access, we do not charge authors for publication.

Paper Evaluation Criteria

SIGMA has two article styles: regular article and review article.

Manuscripts submitted as regular articles are expected to be
- new and original;
- well organized and clearly written;
- of interest to the scientific community;
- not published previously and not under consideration for publication in any other journal or book.

Review articles are welcome too. Review articles are critical evaluations of material that has already been published. By organizing, integrating and evaluating previously published material, the author of a review article considers the progress of current research toward clarifying a problem. In a sense, a review article is tutorial in that the author
- defines and clarifies the problem;
- summarizes previous investigations in order to inform the reader of the state of current research;
- identifies relations, contradictions, gaps, and inconsistencies in the literature;
- and suggests a next step or steps in solving the problem.

Refereeing Papers for SIGMA

All the papers submitted to SIGMA are sent for refereeing to at least 2 experts in the specific areas for evaluation according to the above criteria. These referees can either review the papers themselves or recommend other referee(s).

To ensure comprehensive refereeing and to avoid conflicts of interest we choose the referees having in mind:

  • not to involve as referees people that were co-authors of any of the paper's author in the recent years; moreover, we try to ensure that a referee and an author of the paper are not co-authors of the same person.
  • a referee of a paper should not be a co-author of another referee of the same paper in the recent years; moreover, we try to ensure that the referees of the paper are not co-authors of the same person.

We strive to ensure an adequate refereeing and selection process. At the moment around 60 percent of the submitted papers are rejected. Most of the accepted papers have been corrected in accordance with the referees' recommendations.

We monitor any possibility for conflicts of interest in the selection of the referees. Please also inform us if such conflicts arise.

Please contact the Editors for questions about the editorial process and our refereeing policy.

Special thematic issues in SIGMA

SIGMA welcomes proposals from potential Guest Editors for special thematic issues of the journal.

We would like to stress that all papers in the special issues should be original: they should not be simply reviews of authors' own work that is already published elsewhere. Acception of the paper is subject to the results of the peer review process according to regular refereeing rules of SIGMA (see the items above).

If you have any ideas for special issue in SIGMA, please contact us for further consideration.

SIGMA is arXiv overlay

That means that all published articles in the journal have been contributed or will be contributed to the arXiv. In addition, the SIGMA web site has hyperlinks to the arXiv copies.

You can also search or browse SIGMA articles within the arXiv, for example by following this link. As a consequence of the overlay arrangement, SIGMA shares the commitment of arXiv to remain permanently and freely available on the Internet.

If a paper accepted for publication is already on arXiv, the author should give the Editors both the paper number and the password so that we can replace it with the typeset version.

Indexing & Abstracting

SIGMA is covered by the following indexing and abstracting databases:

Copyright Issues

The authors retain ownership of the copyright with respect to their papers published in SIGMA under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

Looking for your support/sponsorship

SIGMA is a non-profit, volunteer-run project. The papers are placed for open access, so there is no subscription, and the journal has no revenue.

Having said that, despite open access, we do not charge authors for the publication, as some authors submitting good papers cannot afford paying page charges for various reasons and we do not want to put them at a disadvantage with those who could pay.

Therefore, the journal has no steady sources of funding and operates solely on the basis of the editors' enthusiasm. All work in editing, copy-proofing etc. is done by volunteers on gratuitous basis.

So, if you (or your organization) would like to support us financially, please contact us.

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