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FERMI-DIRAC STATISTICS AND THE FIRST STEPS TOWARDS QUANTUM ELECTRODYNAMICS. First edition, extremely rare offprint, of Dirac s paper, which "is justly seen as a major contribution to quantum theory" (Kragh, p. 36). It introduced his quantum mechanical derivation of what is now called Fermi-Dirac statistics, which describes a distribution of particles (now known as fermions, a name coined by Dirac in 1945) in certain systems containing many identical particles that obey the Pauli exclusion principle meaning that no two of the particles can occupy the same quantum state simultaneously. It also contains Dirac s first steps towards quantum electrodynamics. The paper "will be remembered as the first in which quantum mechanics is brought to bear on statistical mechanics. Recall that the earliest work on quantum statistics, by Bose and by Einstein, predates quantum mechanics. Also, Fermi s introduction of the exclusion principle in statistical problems, though published after the arrival of quantum mechanics, is still executed in the context of the old quantum theory. All these contributions were given their quantum mechanical underpinnings by Dirac, who was, in fact, the first to give the correct justification of Planck s law, which started it all: 'Symmetrical eigenfunctions … give just the Einstein-Bose statistical mechanics . . . (which) leads to Planck s law of black-body radiation " (Pais, p. 6). Dirac s paper is credited "for having laid the foundations of the integration of quantum mechanics and quantum statistics because they introduced the quantum-mechanical expression of the symmetry of a system under exchanges of equal particles. The quantum formalism of exchange symmetry is regarded as having solved at once long-standing difficulties regarding the statistical properties of both equal particles and light quanta by clarifying and legitimizing the previously foggy notion of indistinguishable particles" (Monaldi, p. 125). The second part of the present paper contained the seed of Dirac s invention of quantum electrodynamics, which was brought to fruition a few months later in The Quantum Theory of the Emission and Absorption of Radiation . In the present paper, "Dirac considered a system of atoms subjected to an external perturbation that could vary arbitrarily with the time … [Dirac obtained results] in agreement with the ordinary Einstein theory, that is, with the quantum mechanical derivation of the B coefficients that occurred in Einstein's theory of 1917 [that gave the probability of absorption and stimulated emission of radiation]. Since he made use of a classical description of the electromagnetic field, Dirac was not at the time able to proceed further, and he noted, One cannot take spontaneous emission [i.e. the A coefficients] into account without a more elaborate theory. This more elaborate theory was ready less than half a year later" (Kragh, pp. 120-121). OCLC lists University of Florida only (where Dirac spent his last years). No copy in auction records. Provenance: Bertha Swirles (1903-99) (signature on front wrapper, extensive annotations to lower margins of last two pages of text, including several equations). As an undergraduate at Cambridge Swirles attended lectures by J. J. Thomson and Rutherford. She remained at Cambridge in 1925 to undertake research in mathematical astronomy under the supervision of Ralph Fowler; another of Fowler s research students, a couple of years ahead of Swirles, was Paul Dirac. After periods at Bristol, Imperial College, London, and Manchester, Swirles took up a lectureship in mathematics at Girton College, Cambridge in 1938, where she remained for the rest of her career. The present paper was "Dirac s first published response to Schrödinger s theory [i.e., wave mechanics]. He had corresponded with Heisenberg while completing his PhD thesis in Cambridge in the spring of 1926. Many years later, he wrote in his recollections that he did the [present] work on many-particle.
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