## Zur Quantendynamik der Wellenfelder, pp. 1-61 in Zeitschrift für Physik, 56. Bd., 1. & 2. Heft, 8 July, 1929 [With:] Zur Quantendynamik der Wellenfelder II, pp. 168-190 in Zeitschrift für Physik 59. Bd., 3. & 4. Heft, 2 January, 1930.

Berlin: Julius Springer, 1929-30.

First edition, journal issues in original printed wrappers, of this two-part paper which represents the “formal invention of quantum electrodynamics [QED]” (Miller, p. xiii). “Three years before the discovery of the positron Heisenberg and Pauli – in two papers ‘Zur Quantenmechanik der Wellenfelder’ and ‘Zur Quantenmechanik der Wellenfelder II’ of 29 March and 7 September 1929, respectively – took a decisive step forward to develop a consistent theory of quantum electrodynamics” (Mehra & Milton, p. 186). “This extremely technical and mathematical branch of quantum physics, the foundations of which were laid by Heisenberg, Dirac, Pauli, Jordan, and their colleagues during the late 1920s and early 1930s, continues to this day with much the same program and approach . . . [Heisenberg was] a leading member of the small band of abstract theorists who established the program and laid the foundations of relativistic quantum field theory as it has been pursued ever since” (Cassidy, p. 276). This paper – the only one that Heisenberg and Pauli co-authored – attempted to establish “a consistent extension of the quantum formalism that would yield a satisfactory unification of quantum mechanics and relativity theory . . . In 1929, drawing upon the work of Dirac, Jordan, Oskar Klein, and others, Heisenberg and Pauli succeeded in formulating a general gauge-invariant relativistic quantum field theory by treating particles and fields as separate entities interacting through the intermediaries of field quanta. The formalism led to the creation of a relativistic quantum electrodynamics, equivalent to that developed by Dirac, which, despite its puzzling negative energy states, seemed satisfactory at low energies and small orders of interaction. But at high energies, where particles approach closer than their radii, the interaction energy diverges to infinity. Even at rest, a lone electron interacting with its own field seemed to possess an infinite self-energy” (DSB, under Heisenberg). “Heisenberg and Pauli were well aware of the shortcomings of their theory: the divergence difficulties and the problem of negative energies for the electron. However, the importance of the Heisenberg-Pauli theory cannot be exaggerated; it opened the road to a general theory of quantized fields and thereby prepared the tools, albeit not perfect ones, for the Pauli-Fermi theory of beta-decay and for the meson theories” (Mehra & Milton, p. 188). The divergence problems were not resolved until the late 1940s, with the advent of the renormalization techniques of Feynman, Schwinger and Tomonaga.

“Soon after reading the manuscript of Dirac’s QED paper [‘The quantum theory of the emission and absorption of radiation,’ *Proceedings of the Royal Society* A114 (1927), pp. 243-265], Pauli embarked on a program to construct his own version of quantum electrodynamics, one in which [unlike in Dirac’s theory] the relativistic-invariance-covariance would be apparent and the relation to Maxwell theory manifest. He evidently outlined his proposal in a letter to Heisenberg that is no longer extant. In February 1927 Heisenberg countered: ‘I agree very much with your program concerning electrodynamics, but not quite concerning the analogy, quantum wave-mechanics: classical mechanics = quantum electrodynamics : classical Maxwell theory. That one must quantize the Maxwell equations to get light quanta and so on à la Dirac, I believe already; but perhaps the de Broglie waves will later also have to be quantized in order to obtain charge and mass and statistics (!!) of electrons and nuclei.’ Pauli and Heisenberg evidently disagreed about what had to be quantized. Heisenberg accepted [Pascual] Jordan’s viewpoint and was prepared to quantize all wave fields – including matter waves. Pauli, on the other hand, was ready to quantize only the electromagnetic field. With that in mind he studied the mathematics of functionals that Vito Volterra had elaborated. On March 12, 1927, Pauli wrote Jordan: ‘I believe that I now have the essential understanding of the Hamilton-Jacobi theory of Maxwell’s equations. My principal source is a (French) book by P. Levy, Leçons d’analyse fonctionelle, Paris, 1922. We will thus see whether I can erect a quantum electrodynamics. For the present I am in good spirits.’ In late March 1927 Pauli sent Bohr a note to inform him that ‘at the moment I am much occupied with quantum electrodynamics … I have written briefly to Heisenberg about my general foundational standpoint about quantum electrodynamics and would very much like to hear from him … (I *dare* not ask you what your opinion is).’ A few days later Pauli received a letter from Heisenberg asking him a couple of things about his ‘Program’: ‘I am in full agreement with the foundations of your program that [the electromagnetic field variables] are not c[ommuting] fields, but are *q* fields, and that they must satisfy commutation rules that express this fact. But …’

“And so began the collaboration between Heisenberg and Pauli that eventually resulted in two important papers, ‘On the quantum dynamics of wave fields,’ that were published in February and September 1929 [sic]. In them a general method for quantizing any field is presented …

“Pauli outlined the scheme in a letter to [Oskar] Klein in mid-February 1929 and included in his letter some of the conclusions Heisenberg and he had reached:

- The theory contains divergences stemming from the self-energy of the charged particles;
- The matter field can seemingly be quantized so as to obey either Fermi or Bose statistics;
- The theory introduces three kinds of fields: the electromagnetic field, the matter field describing electrons, and the matter field describing protons.

“The first of the two lengthy papers Heisenberg and Pauli wrote on the quantum theory of wave fields was received by *Zeitschrift für Physik* on March 19, 1929. Although their correspondence reflects a pessimistic assessment of their paper Pauli and Heisenberg stated that although their theory was provisional they nonetheless believed that the ‘future correct theory’ would exhibit many of the features of the present formalism” (Schweber, pp. 39-42).

“With their all wave-like theory, Heisenberg and Pauli were able to give a general, though very heavy proof of relativistic invariance. But to what extent did their use of quantized matter waves bring new predictions or new possibilities? If one considers the general quantum field theory they developed, the answer is largely positive: new particles, new fields to be discovered later, with any spin value, could fit into their framework. Above all, processes annihilating or creating matter were allowed … But Heisenberg and Pauli were wrong when they hoped that their theory, once restricted to pure quantum electrodynamics, brought new predictions differing from Dirac’s radiation theory. Pauli even thought that he could give a new estimate of secondary *γ*-ray emission in β-decay explaining the continuity of the β-spectrum. Illusions were soon dispelled. A young American visitor, Robert Oppenheimer, helped Pauli to apply the mathematical transformation that led back to electron configuration space, which was more suitable to describe atomic systems. Then Oppenheimer eliminated the ‘longitudinal photons’ from the Heisenberg-Pauli formalism to reach a new form perfectly equivalent to Dirac's original radiation theory, except for the use of Dirac’s electron. The incompleteness ascribed by Heisenberg, Pauli, and Fermi to Dirac’s theory proved to be only apparent.

“Worse than that, Pauli and Oppenheimer demonstrated that the self-energy infinities that had been met several times on the way to quantum electrodynamics were not of a purely formal nature; they definitely spoiled physical things like line spectra. In July 1929 Pauli wrote to Bohr:

Two complete journal issues, 8vo (229 x 156 mm). Original printed wrappers (some light wear to the spine strip of the first issue and two small pieces missing from the lower left corner, front and rear). A near fine set with no stamps or other markings.

Item #2627

**
Price:
$2,850.00
**