Quantum fields theory (Q2769107)

This book arose from an introductory course in quantum field theory given in several institutions at Switzerland.NEWLINENEWLINENEWLINEChapter one provides the tools which will be used later in quantum field theory: the action functional, the Lagrangian formalism, the symmetries of the action and related conservation laws. These symmetries encode physical information. Gauge invariance is introduced and it is seen how it allows a classification of fields. A Lagrangian density as complete as possible is proposed at the end: it contains several terms with their associated gauge transformations. Chapter two is devoted to the canonical quantization of a free field. It can be a scalar (real or complex), spinorial or a gauge field. Covariance issues in the latter quantification procedure are considered. Correspondingly, one describes the propagation of particles with associated Green functions. In contrast, the next chapter deals with interactions and due to the resulting nonlinearities, one cannot use the solution method via Fourier expansions. But one gets an approximation to the free case in the asymptotic situation (time tends to \(\pm\infty\)). The \(S\) matrix methods constructs probabilities for transitions between the asymptotic free situations. The calculation procedure involves Green functions and Feynman diagrams.NEWLINENEWLINENEWLINEChapter four describes phenomenolgical aspects of the Lagrangian densities for strong, weak and electromagnetic interactions of elementary particles. Special attention is paid here to discrete symmetries: charge conjugation, parity, time reversal \((C,P,T)\). This chapter thus broadens the perspective opened by the two previous ones.NEWLINENEWLINENEWLINEChapter five applies the theories developed earlier to several physical situations: electron-positon annihilation, Compton diffusion, \(W^{\pm}\) and disintegration, muon disintegration, deep inelastic scattering, disintegration of the Higgs boson in two photons. The next chapter explores the difficulties posed by the perturbative method of chapter three. Interactions are seen as perturbations, but some terms lead to diverging integrals. Renormalization is an attempt to repair this situation by using balancing terms so that the resulting integrals converge at all orders. Here one focuses on the Abelian gauge case, with one loop in quantum electrodynamics. Chapter seven deals with symmetry breaking of gauge symmetries. One looks at the generation of massive particles and at the Higgs mechanism. The final chapter presents the standard model of Glashow, Salam and Weinberg. It consists of a Lagrangian density with symmetries associated to various interactions (strong, weak-electromagnetic).NEWLINENEWLINENEWLINEAppendices deal with notations, conventions and chiral anomaly. One finds 74 references and an index.NEWLINENEWLINENEWLINEThis clearly written book has excellent pedagogical qualities and can be used as an introductory text to the field for teaching.