The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [group-representations]

Use as a synonym to the representation-theory tag

574 questions
Filter by
Sorted by
Tagged with
22 views

Center of $SU(3)$

I assumed a 3x3 matrix of the form $$A= \begin{pmatrix} a & b & c\\ d & e & f\\ k & l & m \end{pmatrix}$$ Then, since we know that the center is always an Abelian invariant ...
14 views

Inner product on group theoretic coherent states and anti-commutator of Lie algebra generators

This question is related to group theoretic coherent states (Gilmore, Perelomov etc.). I consider a semi-simple Lie group $G$ with Lie algebra $\mathfrak{g}$ and a unitary representation $U(g)$ acting ...
49 views

Co-spinors and contra-spinors

As i was reading my teacher's notes on $SU(2)$ and $SO(3)$, i have had this question. Why do co-spinors transform differently under a rotation than contra-spinors?
59 views

SO(3) and SU(2) [closed]

If we define $$X(\textbf{a} )=e^{(ia_iL_i)} ,$$ how can we show that $X(\textbf{α} )$ can be written as a $2×2$ matrix in terms of 2 complex parameters $a$ and $b$ with $|a|^2 + |b|^2 = 1$, and ...
23 views

Significance of Wigner-Eckart theorem [duplicate]

What is the physical importance of the Wigner-Eckart theorem and are there any examples of its physical application?
76 views

73 views

120 views

62 views

Helicity under rotation

Suppose that the state $|p,\sigma\rangle$ (for a massless particle) has 3 momentum ${\bf p}=p_3$ (that is the momentum is in the $z$ direction) and that $J_3|p,\sigma\rangle=\sigma|p,\sigma\rangle$ ...
30 views

There is a classification of matrix representations of Euclidean group $\mathrm{E}(n)$ (also called $\mathrm{ISO}(n)$)?

I'm wondering if someone has already done a classification of matrix representations of the Euclidean group $\mathrm{E}(n)$, more specifically I'm trying to classify $\mathrm{E}(2)$. I watched a ...
333 views

Why are physicists so interested in irreps if in their non-block-diagonal form they mix all components of a vector?

Consider a group $\{G,\circ\}$, with elements $e,g_1,g_2,...$, represented by the matrices $\{D(e), D(g_1), D(g_2)...\}$. If all the matrices can be brought to block diagonal forms by a similarity ...
35 views

How to make a triplet out of 2 doublets in the $SU(2)$ representation?

In Y.Grossman and Y.Nir "The Standard Model" book in chapter 4 (non abelian symmetrys) they present the law of whom we can have a triplet and singlet out of 2 doublets name them $\phi_a$ and $\phi_b$, ...
29 views

Generators of 2D global conformal group in terms of differential operators?

I'm looking for a reference that lists generators of two dimensional global conformal group on a complex sphere in terms of differential operators that may act on quasi primary fields $\phi(z,\bar z)$....
40 views

66 views

$3+3$ representation of $SO(4)$

In Zee's Group Theory in a Nutshell book, he says that the antisymmetric tensor $A^{ij}$ furnishes a 6 dimensional representation of $SO(4)$. He further argues that this 6 dimensional representation ...
59 views

Representation of Poincaré group

Let's consider the most general Lorentz transformation: $x'^{\mu} = \Lambda^{\mu}_{\ \ \nu} x^{\nu} + a^{\mu}$. These transformations form the Poincaré group. The generators of translations of this ...
39 views

Connection between $2n$ real fermions and $SO(2n)$

In section 11.4 of "Basic Concepts of String Theory" by Blumenhagen et al, they say: Consider a system of $2n$ two-dimensional real fermion (...) transforming as a vector of $SO(2n)$. I guess they ...
Representation of the Lorentz group using matrices of $SL(2,\mathbb{C})$
There is a correspondence between the Lorentz group and the group $SL(2,\mathbb{C})$. To each Lorentz transformation $\Lambda$ we can associate two matrices $\pm A(\Lambda) \in SL(2,\mathbb{C})$ such ...