Feynman 1947 letter on path integral for the Dirac equation
Ted Jacobson
TL;DR
This study analyzes Feynman’s 1947 private letter on constructing a spacetime path integral for the Dirac equation, placing it in the historical path toward a worldline formulation of spin-1/2 propagation. It provides a full transcription and editorial context, emphasizing Feynman’s geometric approach that uses rotations and quaternions to encode spin along worldlines in $3+1$ dimensions and his tentative one-step evolution rule. Although the program is not completed and faces convergence and nonlocality issues, the work illuminates how these private ideas foreshadow the later diagrammatic framework of QED and connect to subsequent developments such as Polyakov’s spin factor and Jacobson’s spinor-based path integrals. The paper also clarifies the influence and limitations of these early ideas in shaping the transition from classical worldline concepts to quantum-field-theoretic propagators. Overall, it highlights the value of private, exploratory work in understanding how Feynman’s trajectory-inspired thinking evolved into the successful, diagrammatic language of modern quantum electrodynamics.
Abstract
In 1947, four months before the famous Shelter Island conference, Richard Feynman wrote a lengthy letter to his former MIT classmate Theodore Welton, reporting on his efforts to develop a path integral describing the propagation of a Dirac particle. While these efforts never came to fruition, and were shortly abandoned in favor of a very different method of dealing with the electron propagator appearing in in QED, the letter is interesting both from the historical viewpoint of revealing what Feynman was thinking about during that period just before the development of QED, and for its scientific ideas. It also contains at the end some philosophical remarks, which Feynman wraps up with the comment, ``Well enough for the baloney.'' In this article I present a transcription of the letter along with editorial notes, and a facsimile of the original handwritten document. I also briefly comment on Feynman's efforts and discuss their relation to some later work.