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Feynman's Operational Calculus and BeyondNoncommutativity and Time-Ordering$
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Gerald W Johnson, Michel L. Lapidus, and Lance Nielsen

Print publication date: 2015

Print ISBN-13: 9780198702498

Published to Oxford Scholarship Online: September 2015

DOI: 10.1093/acprof:oso/9780198702498.001.0001

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Epilogue: Miscellaneous Topics and Possible Extensions

Epilogue: Miscellaneous Topics and Possible Extensions

(p.343) 11 Epilogue: Miscellaneous Topics and Possible Extensions
Feynman's Operational Calculus and Beyond

Gerald W. Johnson

Michel L. Lapidus

Lance Nielsen

Oxford University Press

A brief discussion is given of possible extensions to the theory developed in this book, and suggestions for the direction of future research in this general area are given. This is done via a collection of eleven open problems, of different scopes and levels of difficulty, and discussing possible techniques and directions of investigation. They involve many different areas and fields of pure mathematics, applied mathematics and theoretical physics, including functional analysis, operator theory, semigroup theory, operator algebras, harmonic analysis, probability theory, differential and partial differential equations, real analysis and measure theory, distribution theory, infinite-dimensional stochastic and geometric analysis, multivariable complex analysis, fractal geometry, quantum mechanics and quantum field theory, quantum statistical physics, renormalization theory, supersymmetry, quantum groups, and Hopf algebras, as well as aspects of noncommutative algebra, geometry, combinatorics and probability theory.

Keywords:   disentangling, semigroup, probability, measure, distribution, stochastic, renormalization, Hopf algebra, quantum group

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