Quantum Theory of Fields (until 1947)

Abstract

The basic idea of field quantization is some 60 years old. A particularly clear anticipation of later trends is found in a paper by Ehrenfest (1906). Commenting on Planck’s theory of the Hohlraum radiation, Ehrenfest discusses the thermal equilibrium spectrum by means of the Rayleigh-Jeans normal modes analysis, exploiting the analogy of the amplitude of a proper vibration of the cavity with the coordinate of a material oscillator. Whereas the classical equi-partition of energies leads to the Rayleigh-Jeans spectrum, how can one modify the theory to obtain the Planck spectrum? As a possibility, suggested by Planck’s quantization of material oscillators, Ehrenfest mentions the following hypothesis: the amounts of field energy residing in a normal mode of frequency v can only be integral multiples of hv. The same assumption enabled Debye (1910) actually to derive the Planck spectrum. As we know today, such a quantization of the field energy results in exhibiting the corpuscular aspects of the system; but this connection with Einstein’s light quantum hypothesis (1905) remained obscure until much later. Once the wave-particle dualism was understood, after the advent of wave mechanics, Debye’s theory was seen to be equivalent to Bose’s photon gas statistics (1924). The characteristic features of Bose’s counting of states (namely, a permutation of n identical photons does not give a new state) corresponds to the non-degeneracy of the quantum state n of a linear oscillator (Born, Heisenberg and Jordan, 1926).

Editor’s note: Professor Gregor Wentzel was the chairman of the session devoted to quantum field theory at our symposium. We had invited him to contribute a paper on the historical development of quantum field theory, but the circumstance that he now lives in retirement in Ascona, Switzerland, without easy access to reference journals, prevented him from doing so. Professor Wentzel has had a long and distinguished association with this subject, and he has exercised a profound influence on its development. For this reason, as well as to provide a detailed conceptual background of the development of this subject from its origin until 1947, we are reprinting Professor Wentzel’s authoritative article. [Reprinted from: M. Fierz and V. F. Weisskopf (Editors), Theoretical Physics in the Twentieth Century, Interscience Publishers, New York and London (1960), pp. 48–77, by permission of John Wiley and Sons, Inc., Publishers, New York.]