Introduction to Quantum Field Theory and the Standard Model

The following sections are included:

• Preface
• Contents

It is a assumed that the reader is already familiar with special relativity, e.g. at the level of a first course on electrodynamics. Thus, this chapter serves essentially as a summary of the relevant theoretical ingredients, to introduce notations and conventions, and to provide the classical basis for advancing to quantum theory in the subseqent chapters…

The quantum mechanical description of particles in accordance with the principles of relativity, relativistic quantum mechanics, turns out to be a problematic concept with fundamental difficulties that are finally based on the equivalence of mass and energy resulting in non-conserved particle numbers…

Quantum electrodynamics (QED) is the fundamental theory of the electromagnetic interaction. Historically QED was invented to describe the interaction of electrons and positrons with photons. Today QED in a wider sense describes the interaction of photons with fundamental charged Dirac particles, such as e^±, μ^±, τ^±, and quarks.

The Lagrangian formulation of mechanics and field theory is a particularly suitable framework for the description of physical systems. A multitude of reasons can be given for the Lagrangian approach…

Quantum chromodynamics (QCD) is the fundamental theory of the strong interaction, at the level of the building blocks of hadronic matter, the quarks. It is a gauge invariant quantum field theory with the gauge group SU(3).

After the electromagnetic and the strong interaction the third fundamental force, the weak interaction, requires an adequate theoretical description. As it turns out, a consistent fomulation is only possible in combination with QED, which amounts to a unification of the electromagnetic and the weak interaction in terms of a common “electroweak interaction”. As in the previous cases, the basic ansatz follows the principles for a description within the framework of a gauge theory, but immediately a central problem occurs: the gauge bosons W^±, Z⁰ corresponding to the weak interaction are not massless, as required by gauge symmetry. A new concept is needed in order to reconcile local gauge invariance and massive gauge bosons: the Higgs mechanism. Moreover, also the masses of the charged leptons and quarks are in a conflict with gauge symmetry because of the missing left–right symmetry of the weak interaction. A solution of this conflict is achieved with the help of a Yukawa interaction that has to be introduced in addition. The gauge theory of the electroweak interaction with all these special features is by now commonly accepted and named the electroweak Standard Model.

The following sections are included:

• Bibliography
• Index