Functional Analysis And The Feynman Operator Calculus
by Tepper Gill /
2016 / English / PDF
3.7 MB Download
This book provides the mathematical foundations for Feynman's
operator calculus and for the Feynman path integral formulation
of quantum mechanics as a natural extension of analysis and
functional analysis to the infinite-dimensional
setting. In one application, the results are used to
prove the last two remaining conjectures of Freeman Dyson for
quantum electrodynamics. In another application, the
results are used to unify methods and weaken domain requirements
for non-autonomous evolution equations. Other
applications include a general theory of Lebesgue measure on
Banach spaces with a Schauder basis and a new approach to the
structure theory of operators on uniformly convex Banach spaces.
This book is intended for advanced graduate students and
researchers.
This book provides the mathematical foundations for Feynman's
operator calculus and for the Feynman path integral formulation
of quantum mechanics as a natural extension of analysis and
functional analysis to the infinite-dimensional
setting. In one application, the results are used to
prove the last two remaining conjectures of Freeman Dyson for
quantum electrodynamics. In another application, the
results are used to unify methods and weaken domain requirements
for non-autonomous evolution equations. Other
applications include a general theory of Lebesgue measure on
Banach spaces with a Schauder basis and a new approach to the
structure theory of operators on uniformly convex Banach spaces.
This book is intended for advanced graduate students and
researchers.
