'The Theory of Positrons' & 'Space-Time Approach to Quantum Electrodynamics,' in: Physical Review, Second Series, Volume 76, Number 6, pp. 749-759 & 769-789, September 15, 1949. This item is unavailable.'The Theory of Positrons' & 'Space-Time Approach to Quantum Electrodynamics,' in: Physical Review, Second Series, Volume 76, Number 6, pp. 749-759 & 769-789, September 15, 1949

The Foundations of Quantum Electrodynamics. First edition, journal issue in original printed wrappers, of Feynman's formulation of quantum electrodynamics (QED), involving the famous 'Feynman diagrams.' QED is the quantum theory of the interactions between electrically charged particles and the electromagnetic field (between electrons, positrons and photons, for example). It has been called "the jewel of physics" because of the extreme accuracy of its predictions: for example, the value of the magnetic moment of the electron calculated from QED agrees with the measured value to within a few parts in 100,000,000,000. QED was born in 1928, with Dirac's paper 'The quantum theory of the emission and absorption of radiation.' Although a major advance, this theory, and its development over the next decade by Heisenberg, Jordan, Pauli and others, encountered serious difficulties: it predicted an infinite self-energy for the electron, and several other such 'divergences' (analogous difficulties were already well known in classical electrodynamics). The solution to these problems was provided independently by Feynman, Julian Schwinger and Sin-Itiro Tomonaga, to whom the 1965 Nobel Prize in physics was awarded "for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles." "While Feynman made many original and imaginative contributions to theoretical physics, it may well be that his place in the history of science will be largely based on his approach to renormalizing quantum electrodynamics (QED), and especially on the tools that he invented to accomplish that goal, such as path integrals, the operator calculus, and the famous Feynman diagrams" (Selected Papers, p. 7). Schwinger later wrote: "Like the silicon chip of more recent years, the Feynman diagram was bringing computation to the masses" (Brown & Hoddesdon, p. 329). In 1973, the great Dutch theoretical physicist and Nobel laureate Gerardus t'Hooft commented (CERN 79-9): "Few physicists object nowadays to the idea that diagrams contain more truth than the underlying formalism." "QED explains the force of electromagnetism ? the physical force that causes like charges to repel each other and opposite charges to attract ? at the quantum-mechanical level. In QED, electrons and other fundamental particles exchange virtual photons ? ghostlike particles of light ? which serve as carriers of this force. A virtual particle is one that has borrowed energy from the vacuum, briefly shimmering into existence literally from nothing. Virtual particles must pay back the borrowed energy quickly, popping out of existence again, on a time scale set by Werner Heisenberg's uncertainty principle. "Two terrific problems marred physicists' efforts to make QED calculations. First, as they had known since the early 1930s, QED produced unphysical infinities, rather than finite answers, when pushed beyond its simplest approximations. When posing what seemed like straightforward questions ? for instance, what is the probability that two electrons will scatter? ? theorists could scrape together reasonable answers with rough-and-ready approximations. But as soon as they tried to push their calculations further, to refine their starting approximations, the equations broke down. The problem was that the force-carrying virtual photons could borrow any amount of energy whatsoever, even infinite energy, as long as they paid it back quickly enough. Infinities began cropping up throughout the theorists' equations, and their calculations kept returning infinity as an answer, rather than the finite quantity needed to answer the question at hand. "A second problem lurked within theorists' attempts to calculate with QED: The formalism was notoriously cumbersome, an algebraic nightmare of distinct terms to track and evaluate. In principle, electrons could interact with each other by shooting any number of virtual photons back and forth. The more photons in.…