Partial dynamical symmetries

A. Leviatan*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

60 Scopus citations


This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify interactions, of a given order, with such intermediate symmetry structure. Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the framework of models based on spectrum generating algebras. PDSs of various types are shown to be relevant to nuclear spectroscopy, quantum phase transitions and systems with mixed chaotic and regular dynamics.

Original languageAmerican English
Pages (from-to)93-143
Number of pages51
JournalProgress in Particle and Nuclear Physics
Issue number1
StatePublished - Jan 2011

Bibliographical note

Funding Information:
The author is pleased to acknowledge a fruitful collaboration with Y. Alhassid, J. Escher, J.E. García-Ramos, J.N. Ginocchio, I. Sinai, M. Mamistvalov, P. Van Isacker and N.D. Whelan. Valuable discussions with F. Iachello, D.J. Rowe and I. Talmi on fundamental aspects of partial symmetries, and with R.F. Casten and N. Pietralla on their empirical manifestations, are much appreciated. To them and to many other colleagues who have shown interest in this avenue of research, my warm thanks. This work was supported in part by the Israel Science Foundation and in part by the US–Israel Binational Science Foundation.


  • Algebraic models
  • Dynamical symmetry
  • Pairing and seniority
  • Partial symmetry
  • Quantum phase transitions
  • Regularity and chaos


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