The Dirac-Jordan Transformation Theory—From Matrix Mechanics to Wave Mechanics

Anthony Duncan A, Michel Janssen B

Abstract This chapter covers the emergence of the statistical interpretation of the new quantum mechanics. After covering the earliest suggestions in this direction by Born and Pauli, it covers the statistical transformation theory of Dirac and Jordan, focusing on Jordan’s version. This version was an important part of the inspiration of Heisenberg’s uncertainty paper, which is covered next. The chapter concludes with the Como and Solvay conferences of late 1927 where Bohr revealed his complementarity principle and where the Copenhagen-Göttingen matrix-mechanics camp of Bohr, Born, Heisenberg, and Pauli squared off with Schrödinger, Einstein, De Broglie, and others in the wave-mechanics camp over the interpretation of the new quantum formalism.

Bartel Leenert van der Waerden

John von Neumann

This chapter presents the origins of the transformation theory and related concepts. It shows how, in 1925, a procedure initiated by Werner Heisenberg was developed by himself, Max Born, Pascual Jordan, and a little later by Paul Dirac, into a new system of quantum theory—the first complete system of quantum theory which physics has possessed. A little later Erwin Schrödinger developed the “wave mechanics” from an entirely different starting point. This accomplished the same ends, and soon proved to be equivalent to the Heisenberg, Born, Jordan, and Dirac system. On the basis of the Born statistical interpretation of the quantum theoretical description of nature, it was possible for Dirac and Jordan to join the two theories into one, the “transformation theory,” in which they make possible a grasp of physical problems which is especially simple mathematically.

Robert Golub, S. K. Lamoreaux

Abstract We continue the discussion of the abstract transformation theory which led to the development of second quantization. Jordan had already suggested (in the foundational papers on matrix mechanics by Heisenberg, Born, and himself) that the electromagnetic field should be represented by a matrix, i.e., quantized. Dirac eventually took up this idea and proposed quantizing the field by treating the field as an operator. Jordan (with others) showed how the same technique could be applied to Bosons and then Fermions. This established the roots of quantum field theory. It also cleared up some of the interpretational issues of the time.

S. G. Eckstein, B. B. Varga, S. Ø. Aks