3
votes
2answers
79 views

Why do the states of a spin multiplet have to have the same symmetry?

This was said in Prof. Balakrishnan lecture 19 on quantum mechanics for the case of exchange symmetry, but he showed no reason why. For example, the system corresponding to two spin $\frac{1}{2}$ ...
3
votes
1answer
217 views

Is the spin-rotation symmetry of Kitaev model $D_2$ or $Q_8$?

It is known that the Kitaev Hamiltonian and its spin-liquid ground state both break the $SU(2)$ spin-rotation symmetry. So what's the spin-rotation-symmetry group for the Kitaev model? It's obvious ...
3
votes
1answer
150 views

Why does total spin conservation law forbid the spin wave gap in Heisenberg magnets?

What is the explanation for total spin conservation forbidding the spin wave gap in Heisenberg magnets?
6
votes
1answer
330 views

Do spin-spin interactions break time reversal symmetry?

I'm sure the answer is yes, but how is this shown? Normally for a single spin-1/2 you have a time reversal operator: $-i \sigma_y \hat{K}$ where $\sigma_y$ is the second Pauli matrix and $\hat{K}$ is ...
3
votes
1answer
196 views

Possible states for two electrons in the helium atom

Consider the helium atom with two electrons, but ignore coupling of angular momenta, relativistic effects, etc. The spin state of the system is a combination of the triplet states and the singlet ...
2
votes
1answer
360 views

Baryon wave function symmetry

If a baryon wavefunction is $\Psi = \psi_{spatial} \psi_{colour} \psi_{flavour} \psi_{spin}$, and we consider the ground state (L=0) only. We know that the whole thing has to be antisymmetric under ...
3
votes
1answer
317 views

Constructing the “most general” two-particle spin interaction with $SU(2)$ symmetry

Suppose I want to write down an interaction term for an action for spin 1/2 fermions that is $SU(2)$-symmetric. I start from the most naive general form of such an action: $$S_{int} ~=~ \int_{4321} ...
5
votes
3answers
399 views

The Asymmetry between Real and Imaginary in the three Pauli Spin Matrices

The Pauli spin matrices $$ \sigma_1 ~=~ (\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix}), \qquad\qquad \sigma_2 ~=~ (\begin{smallmatrix} 0 & -i \\ i & 0 ...
10
votes
2answers
493 views

Groups acting on physics - a clarification on electrons and spin

My first question is fairly basic, but I would like to clarify my understanding. The second question is to turn this into something worth answering. Consider a relativistic electron, described by a ...