Embed Size (px)
Citation preview
We have already seen that symmetry plays a fundamental role in determining the form of the Lagrangian, and hence the dynamics, of a theory. We have so far encountered some simple ones, such as the discrete Z2 acting on scalar fields, and the U(1) rotation acting on fermions and complex scalars.
However, actual symmetries in Nature can be more complicated than these ones. Famously, the symmetries of crystals can be described by a set of quite complicated transformations of the lattice. In particle physics, we will encounter a set of different symmetries.
For this, we take a little detour from our discussion on particle physics to introduce some mathematical tools to handle these symmetries. This subject is called group theory.
To describe some symmetry, we need a set of objects that the symmetry acts on, called a basis. We also need specify how the symmetry transformation (group element) acts on the basis, this is called a representation of the group. Often, with some abuse of terminology, we also called the basis a representation. Instead of talking about group theory in an abstract way (there are actually a lot of abstract things one can say about groups), we will focus on the group representation theory.
Group theory is a deep subject. This is not the place to get into the details. We will not focus on mathematical rigor, and we will only give some simple introduction to some useful results mostly by going through examples.
Group theory.Wednesday, May 4, 2016 11:09 PM
grouptheory Page 1
Wednesday, May 4, 2016 11:29 PM
grouptheory Page 2
Wednesday, May 4, 2016 11:32 PM
grouptheory Page 3
Thursday, May 5, 2016 12:10 AM
grouptheory Page 4
Friday, May 6, 2016 12:18 PM
grouptheory Page 5
Friday, May 6, 2016 1:48 PM
grouptheory Page 6
Friday, May 6, 2016 2:00 PM
grouptheory Page 7
Friday, May 6, 2016 2:22 PM
grouptheory Page 8
Friday, May 6, 2016 2:33 PM
grouptheory Page 9
Friday, May 6, 2016 2:47 PM
grouptheory Page 10
Friday, May 6, 2016 3:10 PM
grouptheory Page 11
Friday, May 6, 2016 3:31 PM
grouptheory Page 12
Friday, May 6, 2016 3:45 PM
grouptheory Page 13
Friday, May 6, 2016 3:59 PM
grouptheory Page 14
Friday, May 6, 2016 4:05 PM
grouptheory Page 15
