Scalar quantum electrodynamics is constructed by promoting a global U(1) symmetry to alocal one. We address electrically charged infraparticles, and the correspondingsuperselection sectors, in infinite volume and in finite volume with two kinds of boundaryConditions.

By means of an ion crystal model, we illustrate the concepts of a particle in the senseof quantum mechanics and of quantum field theory. The latter describes reality in particlephysics, but in order to avoid confusion, we temporarily denote it as a “wavicle”.

Chiral symmetry of free fermions is studied in the continuum and on the lattice. In thelatter case, we review the fermion doubling problem and the Nielsen–Ninomiya theorem, thenwe construct Wilson fermions and finally several types of Ginsparg–Wilson fermions, whichare endowed with an exact, lattice modified chiral symmetry.

Scalar field theory is quantized canonically. We also discuss the Noether current at theclassical level and the vacuum energy at the quantum level.

This chapter deals with the renormalization group in Wilson’s spirit. General concepts,like fixed points, are illustrated with examples, such as block-variable transformations,perfect lattice actions, the Wilson–Fisher fixed points, the Callan–Symanzik equation, andvarious scenarios for running couplings.

The free electromagnetic field is quantized canonically and with the functionalintegral. We emphasize the roles of the Gauss law, helicity, and gauge fixing in thecontinuum. We also derive Planck’s formula for black-body radiation and apply it to thecosmic microwave background.

In high-energy scattering processes, hadrons can be described as a set of partons. Thispicture is compatible with QCD, where the partons are identified as quarks, anti-quarks,and gluons. In this picture, we consider electron–positron annihilation, which can lead tohadrons or a muon–anti-muon pair. The R-ratio of the cross sections for these scenariosallows us to identify the number of colors, Nc = 3, experimentally. Next we discuss deep inelasticelectron–nucleon scattering, which leads to the concepts of the Bjorken variable,structure functions, the parton distribution function, Bjorken scaling, the Callan–Grossrelation, and the DGLAP evolution equation. The hadronic tensor takes us to the scalingfunctions, where high-energy neutrino–nucleon scattering provides further insight, inparticular a set of constraints which are expressed as sum rules.

Starting from 2-flavor QCD, isospin symmetry is employed in order to explain themultiplets of light baryons and mesons, from a constituent quark perspective. Next weinvolve the strange quark and arrive at meson mixing as well as the Gell-Mann–Okuboformula for the baryon multiplet splitting. Regarding QCD from first principles, wecomment on lattice simulation results for the hadron masses. At last we discuss the hadronspectrum in a hypothetical world with Nc=5colors.

The fermion content of the Standard Model is extended to 3 generations. For the leptonwe discuss universality, and for the quarks the GIM mechanism, the CKM quark mixingmatrix, and its CP violating parameter. Similarly, for the leptons we construct the PMNSmixing matrix, and we describe how neutrino oscillation was observed. Since the StandardModel is complete now, we provide an overview over its parameters and take another lookfrom an unconventional low-energy perspective.

This chapter first focuses on the QCD vacuum θ and the related strong CP problem. Wereview the manifestation of theta in the QCD action or alternatively in the mass matrix,and in chiral perturbation theory. Beyond the Standard Model, the Peccei–Quinn formalismturns θ into an axion field. We discuss that approach and its implications in astrophysicsand cosmology. Finally we consider the corresponding parameters for the SU(2)L gauge field and forQED. The former can be absorbed by field-redefinitions, but the latter leads to a linearcombination of these two vacuum angles, which persists as a parameter of the StandardModel, but which is often ignored.

The Standard Model is reduced to Quantum Chromodynamics (QCD) only by a limitation tomoderate energies. We review crucial properties like asymptotic free and the role ofchiral symmetry. The latter is analyzed both in the continuum and on the lattice. Inparticular, the Ginsparg–Wilson relation for lattice Dirac operators allow us to properlyaddress the hierarchy problem which appears fermion masses at the non-perturbativelevel.

The gluon SU(3) gauge field is studied, with “quarks” only as static sources. Wedescribe confinement by referring to the Wegner–Wilson loop and its strong-couplingexpansion on the lattice. The way back to the continuum is related to asymptotic freedom.We discuss the strength of the strong interaction, its low-energy string picture, and theLuescher term as a Casimir effect. The Fredenhagen–Marcu operator provides a soundconfinement criterion. In the confined phase we discuss the glueball spectrum, thePolyakov loop, and center symmetry. We also consider deconfinement at high temperature,and finally the case of a G(2) gauge group instead of SU(3).

We sketch the highlights of Part I, which introduces the concepts of quantum fieldtheory.