Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman’s operational calculus

  title={Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman’s operational calculus},
  author={Gerald W. Johnson and Michel L. Lapidus},
  journal={Memoirs of the American Mathematical Society},
© Annales mathématiques Blaise Pascal, 1996, tous droits réservés. L’accès aux archives de la revue « Annales mathématiques Blaise Pascal » (http: // implique l’accord avec les conditions générales d’utilisation ( Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. 
The Feynman integral and Feynman's operational calculus: a heuristic and mathematical introduction
© Annales mathématiques Blaise Pascal, 1996, tous droits réservés. L’accès aux archives de la revue « Annales mathématiques Blaise Pascal » (http: // implique l’accord
Feynman’s operational calculi for noncommuting operators: The monogenic calculus
In recent papers the authors presented their approach to Feynman’s operational calculi for a system of not necessarily commuting bounded linear operators acting on a Banach space. The central objects
Path Integrals, Fourier Transforms, and Feynman's Operational Calculus
Abstract. The disentangling process is the key to Feynman's operational calculus for noncommuting operators. The main result of his heuristic calculations deals with disentangling an exponential
Combining Continuous and Discrete Phenomena for Feynman’s Operational Calculus in the Presence of a ($${\varvec{C}}_{\mathbf{0 }}$$C0) Semigroup and Feynman–Kac Formulas with Lebesgue–Stieltjes Measures
This paper introduces the presence of a $$(C_{0})$$(C0) semigroup of linear operators into the disentangling of functions of noncommuting operators in the setting where time-ordering measures with
Time Maps in the Study of Feynman’s Operational Calculus via Wiener and Feynman Path Integrals
It is known that Wiener and Feynman path integrals provide one way of making Feynman’s heuristic operational calculus for noncommuting operators mathematically rigorous. The disentangling process and
We study Feynman's Operational Calculus for operator- valued functions of time and for measures which are not necessarily probability measures; we also permit the presence of certain un- bounded
Foundations for relativistic quantum theory. I. Feynman’s operator calculus and the Dyson conjectures
In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series
Feynman’s Operational Calculi: Disentangling Away from the Origin
In this paper we develop a method of forming functions of noncommuting operators (or disentangling) using functions that are not necessarily analytic at the origin in ℂn. The method of disentangling
Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus: The Time Independent Setting
Via a general construction, we are able to establish a quite general and comprehensive stability theory for Feynman’s operational calculus in the time independent setting. In particular, we are able
The Feynman-Kac formula with a Lebesgue-Stieltjes measure: An integral equation in the general case
Let u(t) be the operator associated by path integration with the Feynman-Kac functional in which the time integration is performed with respect to an arbitrary Borel measure η instead of ordinary


Time-ordered operators and Feynman-Dyson algebras
An approach to time‐ordered operators based upon von Neumann’s infinite tensor product Hilbert spaces is used to define Feynman–Dyson algebras. This theory is used to show that a one‐to‐one
Time-ordered operators. II
Apres avoir construit les fondements mathematiques generaux pour des equations d'evolution lineaires en temps ordonne, on applique les resultats pour montrer qu'a la fois le developpement en
The Cameron-Storvick function space integral: an $L(L_{p},L_{p'})$ theory
In [3] Cameron and Storvick introduced a very general operatorvalued function space "integral". In [3-5, 8, 9, 11, 13-20] the existence of this integral as an operator from L2 to L2 was established
Space-Time Approach to Non-Relativistic Quantum Mechanics
Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which
Inverse Problems in Quantum Scattering Theory
The physical importance of inverse problems in quantum scattering theory is clear since all the information we can obtain on nuclear, particle, and subparticle physics is gathered from scattering
Functional integration and quantum physics
Introduction The basic processes Bound state problems Inequalities Magnetic fields and stochastic integrals Asymptotics Other topics References Index Bibliographic supplement Bibliography.
The radiation theories of Tomonaga
  • Schwinger and Feynman, Phys. Rev
  • 1949