Bemerkungen zur Diracschen Theorie des Positrons. Offprint from Zeitsch. f. Physik 90. Kramers's copy

Heisenberg, Werner (1901-76). Bemerkungen zur Diracschen Theorie des Positrons. Offprint from Zeitschrift für Physik 90 (1934). 209-231pp. 231 x 157 mm. Original printed wrappers, detached, front wrapper upper corner torn, some fraying. Good copy. From the library of H. A. Kramers (1894-1952), with his signature in blue pencil on the front wrapper and marginal notes and equations on a few pages.

First Edition, Offprint Issue. This copy is from the library of Dutch physicist H. A. Kramers, one of the major contributors to quantum theory; pages 220-221 are extensively annotated with notes and equations in his hand.

In 1930 and 1931 Dirac published his "holes" theory of protons and electrons, in which he predicted the existence of an "anti-electron"—a prediction confirmed experimentally in 1932 when Carl David Anderson discovered the positron. The following year Heisenberg and Wolfgang Pauli turned their attention to Dirac's holes theory, hoping to incorporate it into a new joint program on quantum electrodynamics. This ended in disappointment—Pauli found it nearly impossible to calculate anything with Dirac's formulae—but Heisenberg suggested a different hole scheme, and after some discussion Pauli proposed that he, Heisenberg and Viktor Weisskopf collaborate on a three-man paper containing the formulation of the general theory. Pauli's plan did not come about, but Heisenberg formulated part of the theory and published it in the present paper, "Remarks on Dirac's theory of the positron."

The paper was in two sections. The first, titled "Visualizable theory of matter waves," Heisenberg "used Dirac's density matrix and the Hartree-Fock approximation explicitly and showed that Dirac's subtraction procedure in the R-matrix (which exhibited symmetry between the electrons and holes) was indeed compatible with the usual conservation laws . . . In the second part—entitled ‘Quantentheorie der Wellenfelder' (Quantum theory of wave fields)—Heisenberg indeed went beyond Dirac's Hartree-Fock approximation method; he especially introduced q-number wave fields and developed both a perturbation method . . . and a different iteration procedure, thereby expanding the Hamiltonian up to the fourth order of the electric charge. As Abraham Pais noted later, ‘Heisenberg gives for the first time the foundations for the quantum electrodynamics of the full Dirac-Maxwell set of equations in the way we know it today'" (Mehra & Rechenberg, The Historical Development of Quantum Theory, 6, pp. 918-919; emphasis ours). This paper is one of eleven early QED papers featured in A. I. Miller's Early Quantum Electrodynamics: A Source Book (1994). Cassidy & Baker, Werner Heisenberg: A Bibliography of his Writings, 1934a.