 #1
phoenix95
Gold Member
 69
 20
Summary:
 SL(2, C), SU(2), SU(3)
Main Question or Discussion Point
I have confusions about representation theory. In the following questions, I will try to express it as best as possible.
For this thread say representation is given as
ρ: L → GL(V)
where L is the Lie group(or symmetry group for a physicist)
GL(V) is the general linear transformations of V(of some dimension)
Questions:
1. Often the irreducible representations are labelled along the columns of Reps, dimensions; see page 20 in this. What do they exactly mean? As I see it reps are the representation space V of the given symmetry group(SU(2) in this case) and dimension is referring to the dimension of V. Am I correct?
2. Each entry in the columns is a new irreducible representation(is this correct?), how does the increase in weight relates to the increase in dimensions? What happens here?
3. Take a look at page 35 of this book(attached): Introduction to quarks and Partons by F. E. Close(1979). There he labels the multiplet by different quark names. By doing this he is constructing a representation space V namely (u, d, s) and the SU(3) group acts on this space, correct? So given a higher dimensional representation space(say the octuplet (1, 1)) how does the SU(3) act on it?
For this thread say representation is given as
ρ: L → GL(V)
where L is the Lie group(or symmetry group for a physicist)
GL(V) is the general linear transformations of V(of some dimension)
Questions:
1. Often the irreducible representations are labelled along the columns of Reps, dimensions; see page 20 in this. What do they exactly mean? As I see it reps are the representation space V of the given symmetry group(SU(2) in this case) and dimension is referring to the dimension of V. Am I correct?
2. Each entry in the columns is a new irreducible representation(is this correct?), how does the increase in weight relates to the increase in dimensions? What happens here?
3. Take a look at page 35 of this book(attached): Introduction to quarks and Partons by F. E. Close(1979). There he labels the multiplet by different quark names. By doing this he is constructing a representation space V namely (u, d, s) and the SU(3) group acts on this space, correct? So given a higher dimensional representation space(say the octuplet (1, 1)) how does the SU(3) act on it?
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