Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter Formulas in JB-Algebras

TL;DR

This paper extends Suzuki type estimates and Lie-Trotter formulas to JB-algebras, providing explicit bounds and generalizations for approximating exponentiated sums in quantum algebraic structures.

Contribution

It introduces Suzuki type approximation formulas for JB-algebras and generalizes Lie-Trotter formulas to multiple elements within these algebras.

Findings

Suzuki type approximation formulas hold in JB-algebras.

Explicit estimation formulas are provided.

Lie-Trotter formulas are extended to multiple elements.

Abstract

Lie-Trotter-Suzuki product formulas are ubiquitous in quantum mechanics, computing, and simulations. Approximating exponentiated sums with Jordan product formulas are investigated in the setting of JB-algebras. We show that the Suzuki type approximation for exponentiated sums holds in JB-algebras, we give explicit estimation formulas, and we deduce three generalizations of Lie-Trotter formulas for arbitrary number elements in such algebras. We also extended the Lie-Trotter formulas in a Jordan Banach algebra from three elements to an arbitrary number of elements.