All Questions
Tagged with group-theory quantum-spin
114
questions
19
votes
5
answers
2k
views
Is intrinsic spin a quantum or/and a relativistic phenomenon?
Ok, this is my reasoning. I am probably making some wrong assumptions here, pls tell me where I am going wrong.
Spin as a quantum phenomenon:
Quantum phenomena disappear as the Planck constant goes to ...
- 309
0
votes
1
answer
59
views
Simplification of $\sum_{a=1}^3\sigma^a_{\alpha\beta} S^a_{\gamma\delta}$ where $\sigma^a,S^a$ are representations of $SU(2)$?
As the question asks, I am dealing with a problem where I'd like to simplify
$$\sum_{a=1}^3 \sigma^a_{\alpha\beta} S^a_{mn}$$
where $\sigma^a$ are the spin-1/2 Paulis and $S^a$ are some higher-spin ...
- 3
1
vote
1
answer
271
views
Projector onto Adjoint and Singlet Representations for $SU(N)$
For $SU(2)$, we can contract two spin-1/2 indices and they break apart into two irreducible representation as (math notation) -
$$
2\otimes2 = 3\oplus 1
$$
that is the triplet and the singlet sector. ...
- 317
0
votes
1
answer
184
views
Are $s > 1/2$ spin matrices unitary and $\det = 1$?
A fact we learn in upper undergraduate/early graduate quantum mechanics is that the set of Pauli matrices (i.e spin-$\frac{1}{2}$ matrices) are generators of the group $SU(2)$. A common definition (...
- 1,713
-1
votes
1
answer
81
views
Confusion about irreps of $SU(N)$: is the "color charge" the same as spin 1?
Sorry if the question is too silly or not well stated, I am happy to clarify any point. Also, my presuppositions can be wrong.
Consider a system of spin-$s$ particles: their spin operators $S_x$, $S_y$...
- 3,014
3
votes
1
answer
113
views
What's the definition of spin for a particle in $d$-dimensional Minkowski spacetime?
Consider a relativistic quantum theory in d-dimensional flat spacetime. Neglecting possible internal symmetries, a particle is defined as a system whose Hilbert space furnishes the support of an ...
- 81
2
votes
1
answer
156
views
Decomposing direct product of spin-$s$ representation into direct sum
Direct product of spin-$s$ representations can be decomposed into direct sum of some other spin-s representation:
$$
\{j\}\otimes\{s\}=\sum_{\oplus l=|j-s|}^{j+s}\{l\}
$$
Howard Georgi gives a hint in ...
- 139
5
votes
1
answer
130
views
Dimension of singlet subspace of $2N$ identical spin-1/2 particles
Consider a quantum system of $2N$ identical spin 1/2 particles, each having a 2D Hilbert space $V$. The total Hilbert space is the tensor product $V^{\otimes 2N} \equiv V \otimes \cdots \otimes V$. ...
- 660
0
votes
1
answer
64
views
The relation between spin and momentum in particle state
In quantum field theory, it seems that when we consider a massive particle's spin degree of freedom, we usually do in the particle's rest frame. And I know the little group will only change spin DOF ...
- 35
0
votes
0
answers
28
views
Time reversal of Bloch waves in photonic crystals
In solid-state physics, I understand that in the case of no spin, the time reversal operator $\hat{T}$ is equal to the complex conjugation operator $\hat{K}$ and in the case with spin, $\hat{T} = \hat{...
- 101
0
votes
1
answer
83
views
How do we relate vectors in spacetime to spin 1 representations of $su(2)$ algebra?
If we look at the representations of the $su(2)$ algebra we can construct a representation for every possible spin as follows
$$|0,0\rangle\,\,\, \text{(spin 0)}$$
$$|-1/2,1/2\rangle,|1/2,1/2\rangle\,\...
- 775
1
vote
0
answers
34
views
Tensor Product of Left Handed Spinor and Right Handed Spinor representations of the group $SU(2)_L \times SU(2)_R$ [duplicate]
From quantum mechanics, we know that the tensor product of two spin-half representations would give us spin-1, and spin-0 reps, i.e,
$$(1/2,0)\otimes(1/2,0)\cong(1,0)\oplus(0,0)$$
I want to know what ...
- 85
0
votes
1
answer
144
views
The Quantum theory of non-relativistic angular momentum in representation theoretic terms
I am trying to understand the Quantum theory of non-relativistic angular momentum in terms of representation theory with full precision. In particular, I would like to deduce that angular momentum is ...
- 2,676
0
votes
0
answers
85
views
What is the rotational symmetry of the theorized spin-2 graviton?
We know and have actually measured in the lab with self-interference neutron experiments the 4π-symmetry (720° rotation Dirac Belt characteristic) of all spin-1/2 particles (except the neutrinos) thus ...
- 4,170
0
votes
1
answer
315
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What does it mean to 'combine' spin 1/2 particles [duplicate]
I'm trying to understand a phenomenon covered in several resources that I think I'm struggling with due to my lack of understanding of its meaning.
The idea is that 2 spin 1/2 particles can combine to ...
- 47