Abstract
The previous two chapters were devoted to introducing the basic ingredients necessary in building up a physical description of elementary particles: the fermion matter fields and the gauge fields responsible for the interactions. The time has come to combine these elements into a description of the physics of elementary particles. The result will be the standard model.
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Notes
- 1.
Here we have to remember that the isospin operators acting on the Hilbert space of three particles have the form \(I_{i}=I_{i}^{(1)}\otimes{\mathbf 1}\otimes{\mathbf 1}+ {\mathbf 1}\otimes I_{i}^{(2)}\otimes {\mathbf 1}+{\mathbf 1}\otimes{\mathbf 1}\otimes I_{i}^{(3)},\) where \(I^{(a)}_{i}\) is the isospin operator acting on the Hilbert space of the a-th particle.
- 2.
At the end of this chapter we will see that this is itself not free of problems. How these are overcome will be explained in Chap. 10.
- 3.
- 4.
A word of warning is in order here. Although denoted by the same letter, the fields in the quark doublets are not necessarily the same ones that appear as the hadron constituents in the quark model. The two are related by a linear combination. This for the time being cryptic remark will find clarification in Chap. 10 (see page 197).
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Álvarez-Gaumé, L., Vázquez-Mozo, M.Á. (2012). Theories and Lagrangians III: The Standard Model. In: An Invitation to Quantum Field Theory. Lecture Notes in Physics, vol 839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23728-7_5
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