English

A note on trigonometric identities involving non-commuting matrices

Mathematical Physics 2017-02-21 v1 math.MP

Abstract

An algorithm is presented for generating successive approximations to trigonometric functions of sums of non-commuting matrices. The resulting expressions involve nested commutators of the respective matrices. The procedure is shown to converge in the convergent domain of the Zassenhaus formula and can be useful in the perturbative treatment of quantum mechanical problems, where exponentials of sums of non-commuting skew-Hermitian matrices frequently appear.

Keywords

Cite

@article{arxiv.1702.06069,
  title  = {A note on trigonometric identities involving non-commuting matrices},
  author = {Ana Arnal and Fernando Casas and Cristina Chiralt},
  journal= {arXiv preprint arXiv:1702.06069},
  year   = {2017}
}

Comments

11 pages, 1 figure

R2 v1 2026-06-22T18:23:13.328Z