Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
Mathematical Physics
2021-09-16 v2 math.MP
Abstract
We consider a class of exponentials in the Weyl-Heisenberg algebra with exponents of type at most linear in coordinates and arbitrary functions of momenta. They are expressed in terms of normal ordering where coordinates stand to the left from momenta. Exponents appearing in normal ordered form satisfy differential equations with boundary conditions that could be solved perturbatively order by order. Two propositions are presented for the Weyl-Heisenberg algebra in 2 dimensions and their generalizations in higher dimensions. These results can be applied to arbitrary noncommutative spaces for construction of star products, coproducts of momenta and twist operators. They can also be related to the BCH formula.
Cite
@article{arxiv.2105.12593,
title = {Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra},
author = {Stjepan Meljanac and Rina Štrajn},
journal= {arXiv preprint arXiv:2105.12593},
year = {2021}
}