# Questions tagged [representation-theory]

The systematic study of group representations, which describe abstract groups in terms of linear transformations of vector spaces, such that group elements or their generators are represented as matrices, reducing group-theoretic problems to linear-algebraic ones.

1,421 questions
Filter by
Sorted by
Tagged with
19 views

### Generators of the (1,2,2) of Pati-Salam

I am working on a project involving breaking SO(10) to its Pati-Salam sub group. In one of the path ways you can use, the broken generators fit in the (6,2,2) of Pati-Salam (recall the Pati-Salam ...
2k views

### Can we do better than “a spinor is something that transforms like a spinor”?

It's common for students to be introduced to tensors as "things that transform like tensors" - that is, their components must transform in a certain way when we change coordinates. However, we can do ...
52 views

### Fundamental representation in Group Theory

I am struggling to understand fundamental representations in Group Theory. I know that the fundamental representation of $SU(N)$, as assigned to a matrix $U=U^i_j \in SU(N)$ can be shown through the ...
73 views

### How do we know there are only 16 Dirac bilinears?

We know there are 5 types of bilinears in 4 dimensions, all of them add up to contribute with 16 independent DoF (degrees of freedom). Namely, these bilinears are known as: scalar (1DoF), pseudoscalar(...
50 views

### Lorentz transformation of the spinor fields

I have been reading the Srednicki's QFT textbook (available online at https://web.physics.ucsb.edu/~mark/qft.html) and in Chapter 34 the left and right-handed spinors are discussed. There is a step in ...
70 views

### Complex conjugate Young Tableaux representation [duplicate]

I have been studying Young Tableaux representation from youtube to represent $2\times 2$ and other examples to in $SU(n)$ symmetry. But i am unable to understand nor able to find relevant answers of ...
34 views

50 views

### PCT Theorem and PCT, spin and statistics, and all that book

I am reading through PCT, spin and statistics, and all that, and trying to understand the construction on page 15 specifically equation (1-26) and the calculations that follows, what I can't see is ...
54 views

### How to prove $Q_u = -2Q_d$ from $SU(5)$?

I'm a beginner, and I'm trying to figure out how to prove that charge of Up quark is equal to 2 times the charge of down quark from the 10 representation of $SU(5)$. Please help.
46 views

### Lorentz Binary Group actions in Spin Statistic theorem: $D[-1] = (-1)^{2j}$ in Novozhilov

In Novozhilov's book "Introduction to Elementary Particle Field Theory" there is a reproduction of Weinberg's S-matrix covariant proof of the Spin Statistics Theorem. I've referenced this in other ...
29 views

### Normalization of Generators of $SU(N)$

I have given a finite-dimensional matrix-representation of $SU(N)$. In this representation, the generators are denoted by $G^{a}$ for $a=1,\dots N^{2}-1$. I have to show that I can choose the ...
97 views

### There are infinitely many equivalent irreducible representations of $SO(3)$ on $\mathbb R^3$ [migrated]

The irreducible representation of $SO(3)$ on $\mathbb R^3$ is the set of the matrices $M$ such that $MM^T=I$ and $\det(M)=1$. But this is not the only one, indeed if $A$ is an invertible matrix then ...
22 views

### Equivalence of the Dirac representation of the Lorentz algebra and its conjugate in even dimensions - Polchinski

In Polchinski's String Theory, Appendix B.1 we look at the smallest irreps of the Clifford algebra in even-dimensional spacetimes $d=2k+2$. In (B.1.16) he defines two operators from the gamma matrices ...
45 views

13 views

### Are all familiar symmetry transformations, when they act on fields, linear? [duplicate]

Consider symmetry transformation acting on a field or a set of fields. For example, a gauge transformation of the form $$\phi^\prime_a(x)=U_{ab}(x)\phi_b(x)$$ where $U(x)$ is a matrix with elements ...
34 views

47 views

### How to prove that different squeezed vacua are the ground states of inequivalent CCR representations?

one can find on wikipedia articles on squeeze operators and squeeze coherent states these squeezed coherent states depend on a squeezed parameter r. the usual coherent states have r = 0 i have to show ...
18 views

### Deriving masses after spontaneous symmetry breaking with a field in a peculiar representation

I am attempting to break the Pati-Salam group $SU(4)_{c'} \times SU(2)_L\times SU(2)_R$ with a field $\psi$ that fits in the following representation: $(4,\bar 2,1)$. My objective is to derive the ...