Abstract
Quantum field theory in its application to electroweak and strong interactions has two rather different facets: A pragmatic, empirical one, and an algebraic, systematical one. The pragmatic approach consists in a set of rules and formal calculational procedures which are extremely successful in their application to concrete physical processes, but rest on mathematically shaky ground. The mathematically rigorous approach, in turn, is technically difficult and not very useful, from a practical point of view, for reaching results which can be compared with phenomenology. Generally speaking, quantum field theory quickly becomes rather technical if one wants to understand it in some depth, and goes far beyond the scope of a textbook such as this one. We refer to the many excellent monographs on this topic some of which are listed in the bibliography.
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References
In the early times the pioneers of quantum field theory constructed the perturbation series in the same way as in quantum mechanics. Examples are the calculation of vacuum polarization by Uehling, and the analysis of the Lamb shift by Bethe. (E.A. Uehling, Phys. Rev. 8, 55, 1935; H.A. Bethe, Phys. Rev. 72, 339, 1947). Thus the adjective “modern” for the covariant formulation.
Cf. L.A. Page, Phys. Rev. 106, 394, 1957; V.N. Baier, Enrico Fermi School “Physics with intersecting storage rings”, Academic Press, 1971.
W. Pauli and F. Villars, Rev. Mod. Phys. 21, 434, 1949.
For some early work in which relations of this kind were derived, see H. Rubinstein, R. Socolov, and F. Scheck, Phys. Rev. 154 (1967) 1608.
J. Schwinger, Phys. Rev, 73, 416 (1948).
References to the original theoretical and experimental work are found in the latest edition of the Review of Particle Properties, J. of Physics G: Nucl. Part. Phys. 33 (2006) 1–1231. See also their internet site pdg.lbl.gov, where pdg stands for particle data group.
These formulae can be found, e. g., in the handbook Muon Physics, Vols. I–III, V.W. Hughes and C.S. Wu (eds.), Academic Press 1977.
In fact, this expression may alternatively be derived from what is called a dispersion relation, that is, by means of Cauchy’s integral theorem. In this approach it is the real part of a complex amplitude whose imaginary part describes f + f − creation, see, e. g., G. Källén, Handbuch der Physik, Quantenelektrodynamik, Vol. 1, Springer Berlin-Göttingen-Heidelberg, 1958.
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(2007). Elements of Quantum Electrodynamics and Weak Interactions. In: Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49972-5_10
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