Recently while I was reading a paper on integrability of Rabi model by D Braak. In this paper there is a discussion about the symmetry of a model and that in the case of the Rabi model it is $\mathbb{Z}_{2}$.

Given a Hamiltonian, how can one find the symmetry of the model?

  • $\begingroup$ When you took quantum mechanics, did you learn about the rotational symmetry of the Hamiltonian for the hydrogen atom? $\endgroup$
    – G. Smith
    Commented Jan 13, 2019 at 5:44
  • 2
    $\begingroup$ You can find a general discussion of symmetry in quantum mechanics at en.wikipedia.org/wiki/Symmetry_in_quantum_mechanics. $\endgroup$
    – G. Smith
    Commented Jan 13, 2019 at 5:46
  • 3
    $\begingroup$ The symmetry of a Hamiltonian is not necessarily obvious, and I do not know of an algorithm for finding the maximal symmetry of a Hamiltonian. For example, the symmetry of a hydrogen atom Hamiltonian is actually SO(4), a bigger symmetry group than the obvious SO(3)! $\endgroup$
    – G. Smith
    Commented Jan 13, 2019 at 6:13
  • $\begingroup$ I am sorry, but couldn't get an understanding of the same. I tried to look into one of our reference texts by JJ Sakurai and didn't find a discussion of this there. could you direct me to some any reading? $\endgroup$
    – Fracton
    Commented Jan 16, 2019 at 6:11
  • $\begingroup$ Does Section 4.1 of jultika.oulu.fi/files/nbnfioulu-201512082290.pdf help you? $\endgroup$
    – Ziyuan
    Commented Jan 29 at 14:12


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