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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Feynman's Operational Calculus and Beyond - Noncommutativity and Time-Ordering (Hardcover)
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Feynman's Operational Calculus and Beyond - Noncommutativity and Time-Ordering (Hardcover)
Series: Oxford Mathematical Monographs
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This book is aimed at providing a coherent, essentially
self-contained, rigorous and comprehensive abstract theory of
Feynman's operational calculus for noncommuting operators. Although
it is inspired by Feynman's original heuristic suggestions and
time-ordering rules in his seminal 1951 paper An operator calculus
having applications in quantum electrodynamics, as will be made
abundantly clear in the introduction (Chapter 1) and elsewhere in
the text, the theory developed in this book also goes well beyond
them in a number of directions which were not anticipated in
Feynman's work. Hence, the second part of the main title of this
book. The basic properties of the operational calculus are
developed and certain algebraic and analytic properties of the
operational calculus are explored. Also, the operational calculus
will be seen to possess some pleasant stability properties.
Furthermore, an evolution equation and a generalized integral
equation obeyed by the operational calculus are discussed and
connections with certain analytic Feynman integrals are noted. This
volume is essentially self-contained and we only assume that the
reader has a reasonable, graduate level, background in analysis,
measure theory and functional analysis or operator theory. Much of
the necessary remaining background is supplied in the text itself.
General
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