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Quantum field theory dates back to the same year when matrix and wave mechanics were both founded: indeed, in one of the pioneering papers on matrix mechanics by Born and Jordan (1925), the quantization of the electromagnetic field was considered for the first time. However, the first paper devoted entirely to this topic was that by Dirac (1927), who treated this subject in a systematic manner, and has been henceforth considered to be the founder of "local" quantum field theory (LQFT). The publication of that paper preceded only slightly that of another key paper by Dirac (1928), namely the one in which he launched the equation bearing his name. In the beginning it appeared that the problem of sharp localizability of relativistic quantum particles of spin 1/2 had been thereby solved, but, as discussed in Sections 2.1 and 2.2, subsequent developments proved that hope to have been groundless. In fact, as was pointed out at the end of Section 2.2, Hegerfeldt's (1974) theorem eventually supplied the mathematical proof of the unsolvability of that problem for particles of any spin within the confines of the concept of sharp localizability. The descriptive term "local" has nevertheless remained entrenched in this context, with the phraseology "relativistic quantum field ψ(x) at the spacetime point x" being habitually used ever since Dirac's pioneering work, despite the mathematically proven nonexistence (Bogolubov et al., 1975, Sec. 10.4) of any such entities.

DOI: 10.1007/978-94-009-4492-3_5

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