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This is a set of notes for lectures that were given at TASI2011 in Boulder, Colorado. The notes provide an introduction to next-to-leading order calculations in QCD and develop the spinor calculus necessary for the computation of both tree-level and one-loop amplitudes (using analytic unitarity techniques). A large part of these notes is based on lectures previously delivered by Keith Ellis in W&#252rzburg and Calcutta that were subsequently incorporated into a review article on unitarity techniques. [ABSTRACT FROM AUTHOR]

Shortly after their introduction, the electron's Zweideutigkeit and Pauli's Ausschliessungsregel were embedded into a growing theoretical framework: from Fermi–Dirac statistics in 1926 (Section 4.2), to the non-relativistic quantum mechanics of the magnetic electron with Pauli's spin matrices in 1927 (Section 4.3); from Wigner and von Neumann's group theoretical derivation of the spin matrices in 1927 (Section 4.4), to Jordan's reinterpretation of Pauli's exclusion principle in terms of anticommutation relations for particle creation and annihilation operators in 1928 (Section 4.5), which paved the way for quantum field theory. The most important step in building up this theoretical framework was the transition from non-relativistic to relativistic quantum mechanics, with Dirac's equation for the electron in 1928 (Section 4.6), which finally allowed the derivation of the electron's spin with its anomalous magnetic moment and hence clarified in a conclusive way the origin of spectroscopic anomalies. The negative energy solutions of the Dirac equation, and Dirac's attempt to accommodate them via the hole theory in 1930, anticipated the experimental discovery of the antiparticle of the electron, the positron. Sections 4.7-4.9 reconstruct Pauli's sustained criticism of Dirac's hole theory. The history of this debate is intertwined with Pauli's search for a spin–statistics connection, which finally culminated in the spin–statistics theorem in 1940. With this theorem, the nomological shift from the status of a phenomenological rule to that of a fundamental scientific principle is finally completed. Introduction The year 1925 was the annus mirabilis for quantum mechanics. [ABSTRACT FROM AUTHOR]

The aim of this book was to investigate the rationale for Pauli's principle, and the conditions under which we are justified in regarding a phenomenological and contingent rule as an important scientific principle. To this purpose, I urged a Kantian perspective. As a conclusion, I want to foreshadow how this perspective relates to contemporary discussions about images of science, and how it bears upon the on-going debate on scientific realism in philosophy of science. I shall barely scratch the surface of this complex topic and its vast literature. The best I can do in these concluding remarks is to suggest a philosophical position that I think deserves to be further explored. What follows should then be read more as an outline for future research, than as a conclusion. I began this book by reconstructing the origins of the exclusion principle as a phenomenological rule arising from the spectroscopic research of the 1920s. I argued that the rule was derived – in conjunction with the concept of the electron's Zweideutigkeit – from spectroscopic phenomena with the help of some theoretical assumptions, in the period of revolutionary transition from the old to the new quantum theory. I defended the prospective intelligibility of this revolutionary transition in the light of the piecemeal process of transformation of the old quantum theory, from which brand new scientific concepts and nomic generalizations followed. [ABSTRACT FROM AUTHOR]

This chapter explores the heuristic fruitfulness of the exclusion principle in opening up new avenues of research: namely the idea of ‘coloured’ quarks and the development of quantum chromodynamics (QCD) in the 1960s to 1970s. Sections 5.1 and 5.2 reconstruct the origin of the quark theory from Gell-Mann's so-called ‘eightfold way’ for elementary particles. The experimental discovery of the Ω− particle confirmed the validity of Gell-Mann's model, but it also provided negative evidence against quarks obeying the exclusion principle. Two alternative research programmes emerged in the 1960s to deal with this piece of negative evidence (Section 5.3): the first programme (Section 5.3.1) rejected the strict validity of the exclusion principle and explored the possibility that quarks obeyed parastatistics; the second (Section 5.3.2) retained the exclusion principle and reconciled it with negative evidence by introducing a further degree of freedom for quarks (‘colour’). The Duhem–Quine thesis seems to loom on the horizon (Section 5.4): the choice as to whether questioning the principle or introducing an auxiliary assumption to reconcile it with negative evidence seems to be underdetermined by evidence. However, I shall argue that it was exactly via the development of these two rival research programmes that the exclusion principle came to be validated, and that there was a rationale for retaining the principle despite prima facie recalcitrant evidence. Introduction As we have seen in Chapter 4, soon after 1924 Pauli's exclusion rule was incorporated into the growing quantum mechanical framework, where its role came to be redefined and its nomological scope extended. [ABSTRACT FROM AUTHOR]

This chapter sets the scene for the philosophical analysis of the exclusion principle that I shall carry out in this book. What is the role and function of a scientific principle? Whence does it derive its accreditation and nomological strength? In the philosophical literature on scientific principles, different answers have been given to these questions, from Poincaré's conventionalism to Reichenbach's analysis of coordinating principles. More recently, Michael Friedman has latched onto the latter tradition to defend ‘relativized a priori principles’ as principles that are subject to revision during scientific revolutions, but at the same time maintain a constitutively a priori role within a theoretical framework. This is germane to a reinterpretation of Kant's notion of ‘a priori’, whose purpose is to make a Kantian approach to scientific principles compatible with scientific revolutions and modern scientific developments; whence a resultant ‘dynamic Kantianism’. I shall endorse a suitable version of dynamic Kantianism to investigate the nature of the exclusion principle as playing a ‘regulative’ rather than a ‘constitutive’ function. The regulative/constitutive distinction has a distinguished philosophical pedigree in Kant and in the neo-Kantian tradition of Ernst Cassirer, as I shall spell out in Section 1.4. Introduction In a letter to Alfred Landé on 24 November 1924, Wolfgang Pauli announced an ‘extremely natural prescriptive rule’ that could shed light on some puzzling spectroscopic phenomena he had dealt with in the past three years. The foundation of the rule remained an open question. [ABSTRACT FROM AUTHOR]

The history of the exclusion principle is already an old one, but its conclusion has not yet been written. It is now eighty years since Wolfgang Pauli introduced an ‘extremely natural’ prescriptive rule, while dealing with some spectroscopic anomalies that beset physicists in the heyday of the old quantum theory. The rule excluded the possibility that any two bound electrons in an atom were in the same dynamic state, identified by a set of four quantum numbers. Hence the name of Ausschlieβungsregel (exclusion rule), or Pauli's Verbot (Pauli's veto) as Werner Heisenberg nicknamed it. The far-reaching physical significance of this rule became clear only later. From spectroscopy to atomic physics, from quantum field theory to high-energy physics, there is hardly another scientific principle that has more far-reaching implications than Pauli's exclusion principle. It is thanks to Pauli's principle that one obtains the electronic configurations underlying the classification of chemical elements in Mendeleev's periodic table as well as atomic spectra. To this same principle we credit the statistical behaviour of any half-integral spin particles (protons, neutrons, among many others) and the stability of matter. Shifting to high-energy physics, it is the exclusion principle that fixes the crucial constraint for binding quarks in hadrons, which together with leptons compose our physical world. This book advances a philosophical analysis of the enduring and far-reaching validity of Pauli's principle. It does not aim to address what a scientific principle is. [ABSTRACT FROM AUTHOR]