Analytical evaluation of the numerical coefficients in the Zassenhaus product formula and its applications to quantum and statistical mechanics. (11th May 2019)

• Record Type: Journal Article
• Authors: Bologna, Mauro
• Is Part Of: Progress of theoretical and experimental physics. Volume 2019:Number 5(2019)
• Publication Date: 2019-05-11
• Subjects: A13; Physics -- Periodicals; Mathematical physics -- Periodicals; 530.05
• DOI: 10.1093/ptep/ptz035
• Languages: English
• ISSNs: 2050-3911

Abstract

Abstract: This paper studies the exponential of the sum of two non-commuting operators as an infinite product of exponential operators involving repeated commutators of increasing order. It will be shown how to determine the two coefficients in front of the nested commutators in the Zassenhaus formula. The knowledge of one coefficient is enough to generate closed formulas that have several applications in solving problems ranging from linear differential equations and quantum mechanics to non-linear differential equations.