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TMF, 2008, Volume 155, Number 1, Pages 161–176 (Mi tmf6201)  

This article is cited in 4 scientific papers (total in 4 papers)

Hamiltonian reductions of free particles under polar actions of compact Lie groups

L. Feherab, B. G. Pusztaicd

a University of Szeged
b KFKI Research Institute for Particle and Nuclear Physics
c Université de Montréal
d Concordia University, Department of Mathematics and Statistics

Abstract: We investigate classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds. We describe the reduced systems under the assumption that the underlying compact symmetry group acts in a polar manner in the sense that there exist regularly embedded, closed, connected submanifolds intersecting all orbits orthogonally in the configuration space. Hyperpolar actions on Lie groups and on symmetric spaces lead to families of integrable systems of the spin Calogero–Sutherland type.

Keywords: Hamiltonian reduction, polar action, integrable system

DOI: https://doi.org/10.4213/tmf6201

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English version:
Theoretical and Mathematical Physics, 2008, 155:1, 646–658

Bibliographic databases:


Citation: L. Feher, B. G. Pusztai, “Hamiltonian reductions of free particles under polar actions of compact Lie groups”, TMF, 155:1 (2008), 161–176; Theoret. and Math. Phys., 155:1 (2008), 646–658

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6201
  • http://mi.mathnet.ru/eng/tmf/v155/i1/p161

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Fehér L., Pusztai B.G., “Derivations of the trigonometric $BC_n$ Sutherland model by quantum Hamiltonian reduction”, Rev. Math. Phys., 22:6 (2010), 699–732  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    2. Hochgerner S., “Symmetry Reduction of Brownian Motion and Quantum Calogero–Moser Models”, Stoch. Dyn., 13:1 (2013), 1250007  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    3. Schornerus V., Sobko E., Isachenkov M., “Harmony of spinning conformal blocks”, J. High Energy Phys., 2017, no. 3, 085  crossref  mathscinet  isi  scopus
    4. Schomerus V., Sobko E., “From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models”, J. High Energy Phys., 2018, no. 4, 052  crossref  mathscinet  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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