• Corpus ID: 220936464

Commutators of spectral projections of spin operators

@article{Shabtai2020CommutatorsOS,
  title={Commutators of spectral projections of spin operators},
  author={Ood Shabtai},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
  • Ood Shabtai
  • Published 1 August 2020
  • Mathematics
  • arXiv: Mathematical Physics
We present a proof that the operator norm of the commutator of certain spectral projections associated with spin operators converges to $\frac 1 2$ in the semiclassical limit. The ranges of the projections are spanned by all eigenvectors corresponding to positive eigenvalues. The proof involves the theory of Hankel operators on the Hardy space. A discussion of several analogous results is also included, with an emphasis on the case of finite Heisenberg groups. 
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On polynomials in spectral projections of spin operators

  • Ood Shabtai
  • Mathematics
    Letters in Mathematical Physics
  • 2021
We show that the operator norm of an arbitrary bivariate polynomial, evaluated on certain spectral projections of spin operators, converges to the maximal value in the semiclassical limit. We…

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