4
votes
1answer
63 views

Why must these Spinors be normalized?

I have just begun studying spin and there are two spinors mentioned: The main spinor $\chi $ and the spin-up spin down spinors (eigenspinors) $\chi_+ ,\chi_- $. I learned that the main spinor is a ...
4
votes
1answer
150 views

Helicity and Chirality

Does the concept of both helicity and and chirality make sense for a massive Dirac spinor? A massive electron in chiral basis is written as a column made up of $\psi_L$ and $\psi_R$. What are the ...
3
votes
2answers
196 views

Wavefunction of an electron

Electron is a spin $\frac{1}{2}$ particle, so needs 2-component wave function but the Dirac theory of electron is based on 4-component wave function, are all components of it independent or only two ...
0
votes
1answer
78 views

Why normalizing spin state is different? Why no need dxdydz?

An electron in a spin state: $$X=A\quad\begin{pmatrix} 2i\\2\end{pmatrix}\quad$$ In order to get A, I have to normalise it, my question is how should write? Since I have to normalise why no need ...
1
vote
1answer
239 views

Spinors and Probabilities of Electron-Positron Pair

Question: An electron and positron are moving in opposite directions, and are in the spin singlet state. Two Stern-Gerlach machines are orientated in some ...
1
vote
3answers
928 views

Energy Spectrum of pair of spin-1/2 particles with general Hamiltonian

I found this problem, and so far I am stumped. I was wondering if anyone wanted to solve it with me, or help me calculate eigenvectors, or just give insight on my questions. Consider a system of ...
10
votes
1answer
557 views

What're the relations and differences between slave-fermion and slave-boson formalism?

As we know, in condensed matter theory, especially in dealing with strongly correlated systems, physicists have constructed various "peculiar" slave-fermion and slave-boson theories. For example, For ...
0
votes
0answers
85 views

Finding the coefficients of a spinor

From the Schrödinger equation of a system I'm investigating, where the wave function is a 4-component spinor of coefficients $C_1, C_2, C_3, C_4$, I am able to obtain the expression $\begin{pmatrix} ...
2
votes
2answers
393 views

Two ways to form SU(2) singlets?

I am trying to reconcile the two ways of forming SU(2) singlets out of a pair of doublets. Method (1): If $v=\begin{pmatrix}v^1\\ v^2\end{pmatrix}$ and $w=\begin{pmatrix}w^1\\ w^2\end{pmatrix}$ are ...
0
votes
4answers
784 views

Could one argue that h (Planck constant) and $\hbar$/2 (Dirac constant) are in fact independant constants?

My question is very naive and could sound strange but it seems to me natural in so far as the Planck constant is related to the first quantization (of newtonian particle mechanics/galilean relativity) ...
2
votes
1answer
188 views

How quantum field transforms in case of some particular spin

Except when a particle is spin-0, field of all particles transforms when frame of reference is changed, and this defines what spin is. The question is, specifically how does the quantum field ...
2
votes
1answer
502 views

How to construct the charge conjugation matrix for any given dimension?

Generally, Gamma matrices could be constructed based on the Clifford algebra. \begin{equation} \gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij}, \end{equation} My question is how to generally ...
3
votes
2answers
1k views

parallel/anti-parallel vs. triplet/singlet description of two spins

If we consider two spins, we can think of the spins as being either parallel (up|up or down|down)or anti-parallel (up|down or down|up). Or we can think of them as being in the triplet or singlet ...