Compact exponential product formulas and operator functional derivative

Journal Article · Sat Feb 01 00:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531884· OSTI ID:466884

Suzuki, M ^[1]

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1. Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113 (Japan)

A new scheme for deriving compact expressions of the logarithm of the exponential product is proposed and it is applied to several exponential product formulas. A generalization of the Dynkin{endash}Specht{endash}Wever (DSW) theorem on free Lie elements is given, and it is used to study the relation between the traditional method (based on the DSW theorem) and the present new scheme. The concept of the operator functional derivative is also proposed, and it is applied to ordered exponentials, such as time-evolution operators for time-dependent Hamiltonians. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 466884
• Journal Information: Journal of Mathematical Physics, Vol. 38, Issue 2; Other Information: PBD: Feb 1997
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
HAMILTONIANS
TIME DEPENDENCE
FUNCTIONAL ANALYSIS
FIELD OPERATORS
FUNCTIONALS
LIE GROUPS
QUANTUM MECHANICS