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
    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
    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
    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
    Jan 16, 2019 at 6:11


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.