On the Invariant Regularization in Relativistic Quantum Theory. Offprint from: Reviews of Modern Physics, Vol. 21, No. 3, 1 July 1949. PAULI-VILLARS REGULARIZATION - PRECURSOR TO RENORMALIZATION IN QED

First edition, very rare offprint, of the Pauli-Villars regularization procedure, which is designed to avoid the ultraviolet divergences in quantum electrodynamics (the fact that certain quantities in the theory become infinite, and therefore meaningless in physical terms, due to objects with unbounded energy). From 1946 to 1949, Villars worked as a research assistant at the Swiss Federal Institute. While there, he collaborated with Wolfgang Pauli on work in quantum electrodynamics. "In the infancy of quantum electrodynamics, he and the Swiss Nobel Laureate Wolfgang Pauli developed a simple and elegant method to regulate the mathematical singularities in quantum field theory and extract finite physical results. The resulting method, known as "Pauli-Villars regularization," was widely influential and is known and used by all students of field theory" (Villars' obituary, Physics Today 56 (2003), p. 102). The method is based on earlier work by Richard Feynman, Ernst Stueckelberg and Dominique Rivier. "This paper appeared in the issue of the Reviews of Modern Physics dedicated to Einstein's 70th birthday on 14 March 1949 and for which Abraham Pais had collected the manuscripts. Pais had asked Pauli to write an introduction to the volume, but Pauli felt that he 'actually had done his duty towards Einstein' with his contribution to the 'Einstein Festschrift.' 'Also I feel I am not in as close personal contact as with Bohr, since the pre-history in both cases is quite different for me. As personal an introduction as in the Bohr issue [Vol. 17, nos. 2/3] I cannot write about Einstein'" (Enz, No Time to be Brief (2002), p. 434). Large 8vo, pp. 434-444. Original printed wrappers.…