Tagged Questions

Use as a synonym to the representation-theory tag

1k views

399 views

Is the neutral pion a singlet?

In Griffiths' Introduction to Elementary Particles, it is mentioned p. 179 that the $\pi^0$ is a singlet under $SU(2)$ isospin. But it is also part of the $\pi^-,\pi^0,\pi^+$ isospin triplet. How can ...
271 views

Do generalized Pauli Operators generate SU(n)?

A commonly used generalization of Pauli Operators is the "clock" and "shift" operators summarized here: http://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices Pauli Operators are generators ...
140 views

What is the Physical Significance of Tr(A) w.r.t. Matrix Representations in Group Theory

I've seen the post on mathoverflow.SE asking almost the same question, and I have indeed flipped through said answers, but most are in a more general context ie quantum mechanics and do not provide a ...
133 views

84 views

Where do $L_+$ and $L_-$ live, if not in $\mathfrak{so(3)}$?

This question is continuation to the previous post. The lie algebra of $\mathfrak{so(3)}$ is real Lie-algebra and hence, $L_{\pm} = L_1 \pm i L_2$ don't belong to $\mathfrak{so(3)}$. However, ...
91 views

118 views

Transformation law for spinor functions multiplication

Let's have Dirac spinor $\Psi (x)$, which formally corresponds to $$\left( 0, \frac{1}{2} \right) \oplus \left( \frac{1}{2}, 0 \right)$$ representation of the Lorentz group. What representation is ...
159 views

97 views

Group of translations in two dimensions - A weird treatment

Again, as usual Schwinger leaves me startled as he writes, the Hermitian displacement operator in 2D is $$G = p_1\delta x_1 +p_2 \delta x_2$$ Now, we know clearly that this group is an Abelian ...
479 views

Unitary representations of the diffeomorphism group in curved spacetime

In (special) relativistic quantum mechanics there is a standard argument that says that the (rigged) Hilbert space of states $H$ should be equipped with a projective unitary representation $U$ of the ...