 

Lance Nielsen
Two approaches to the use of unbounded operators in Feynman's operational calculus
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Published: 
April 22, 2020. 
Keywords: 
operational calculus, disentangling, unbounded operators, timeordering,
Taylor calculus, analytic families of operators, stability theory, modified Feynman integral. 
Subject: 
44A99, 47A10, 47A13, 47A60, 47B15, 47B25, 47B48, 46G10. 


Abstract
In this paper, we investigate two approaches to the use of unbounded operators
in Feynman's operational calculus. The first involves using
a functional calculus for unbounded operators introduced by A. E. Taylor
in the paper [34]. The second approach uses analytic families
of closed unbounded operators as discussed in [19]. For each
approach, we discuss the essential properties of the operational calculus
as well as continuity (or stability) properties. Finally, for the approach using the
Taylor calculus, we discussion a connection between Feynman's operational calculus
in this setting with the Modified Feynman Integral of M. L. Lapidus ([14, 20]). 

Acknowledgements
N/A


Author information
Lance Nielsen:
Department of Mathematics
Creighton University
Omaha, NE 68178, USA
lnielsen@creighton.edu

