Lot 75
  • 75


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  • "Classical theory — self energy difficulties. Quantum theory — still in trouble...", ca 1948-49.
Autograph manuscripts, 8 pp on 6 sheets (8 1/2 x 11 in), in pencil on white paper watermarked "Eaton's Cascade Bond Berkshire 11" (3 sheets), on white paper watermarked "Arena Bond" (1 sheet), and on plain white wove paper (2 sheets). Creases where previously folded.

Catalogue Note

Apparently a collection of separate, but likely contemporaneous lecture notes dating to the seminal moment when Feynman pivots from his Fall 1948 papers which invoke Relativistic Cut-Offs for Classical & Quantum Electrodynamics (Phys. Rev. 74, 939 & 1430), and turns, making the revolutionary leap the following Spring, to the celebrated 1949 Nobel Prize-winning work Space-Time Approach to QED (Phys. Rev. 76, 769), in which Feynman diagrams, with their characteristic virtual quanta, appear for the first time in the literature- see Fig. 1,2, etc., therein. The earlier pair of papers were written in the months following the famed Pocono Conference, 29 March-2 April 1948, where Feynman & Schwinger had presented complementary theories of QED and the latter had emerged as victor (Genius, pp.265-258). Nevertheless, Feynman’s Diagrammatica prevailed on the next occasion, the Oldstone Conference, 11-14 April 1949 and he submitted that Nobel paper just 3 weeks later… Feynman looks at the different problems encountered with Classical theory, and indicates where there is still work to be done in Quantum theory. In the first 5 pages or so (on the Eaton's watermarked paper), he cites various attempts to straighten out the Classical theory due to Bom & Infeld, Dirac, Bhabha, Peierls, and Wheeler-Feynman, before writing "The quantization of these have all gotten stuck. I have another way very similar to Peierls, which I can quantize & which does give finite results in Q. Mech...."

He goes on to describe this Classical approach in detail, showing how calculation of the self-energy "Gives infinity."  He then proposes his idea of cutting off this divergence, which yields a finite result, by swapping out the troublesome Dirac delta-function for a "very handy" Bessel function J1, the natural choice by virtue of its simple Fourier transform. In a second section he states "2) Do not have time to go into many beautiful results of this [pair production] but go directly to Q. Mech. Again look at solutions. Start wave function at x...." Later, he continues "What to do for electrodynamics if retarded? Big problem of quantum electrodynamics. Answer is...." In a third section, he continues "3) However there is also self action no one particle.... the effect is to change the phase of the wave func[tion] at B just as a change in mass would..." 

The 4th sheet (on Arena watermarked paper) appears to be an early draft for the first three sheets, as much of the introductory text is the same. 

The last two sheets, on plain wove paper, again treat the difficulties with Quantum Electrodynamics, opening with "Difficulty with Q Elect. that gives infinite self energy. (emit & absorb + Vac Pol). Weiss (& Bethe) scheme diff bound & free. Schwinger formulates which terms renormalize mass. Finish. I make theory, a model for Schwinger, all effects are finite. Advantage of no ambiguity.... He then revisits the Dirac-Bessel swap, taming the divergence in the Classical theory- "Self energy finite "For Dirac eqn., S is operator..." Final of these last two sheets, top- Feynman lays out the situation for Two Particles, initially in non-relativistic setting, but then indicating the necessary refinements to go to fully relativistic treatment; i.e. QED, w/ its tell-tale virtual photons.  The very last equation articulates the mathematical contribution of the infinite Self-Energy Feynman diagram to its left, which can be found as Fig. 2 in the seminal 1949 paper, but may have had, in Feynman’s own hand, a precursor appearance here….