All Questions
Tagged with anticommutator lie-algebra
8
questions
1
vote
1
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Anti-commutator of angular momentum operators for arbitrary spin
I know the commutator of angular momentum operators are
$$
[J_i,J_j]=\mathrm i\hbar \varepsilon_{ijk}J_k.
$$
For spin-1/2 particles, $J_i=\frac\hbar2\sigma_i$ where $\sigma_i$ are Pauli matrices, and ...
- 695
2
votes
1
answer
207
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Are there any 3 or more Hermitian solutions to the problem: $\alpha_i^2=1$, $\{\alpha_i, \alpha_j \}=2$
I’m trying to generate some matrices which are similar to Pauli’s but with the following anti-commutation relation
$$\{\alpha_i, \alpha_j\}=\alpha_i \alpha_j + \alpha_j \alpha_i = 2 \tag{1}$$
And
$$\...
- 2,241
2
votes
1
answer
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Anticommutator of spin-1 matrices
We know that in the spin-1/2 representation the anticommutation relation of the Pauli matrices is $\{\sigma_{a},\sigma_{b}\}=2\delta_{ab}I$. Does a similar relation hold for the spin-1 representation?
0
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203
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Anticommutativity of an anticommutator of supercharges
In this paper, equation 38 gives the ${\cal N}=2$ Super-Poincare (extended with the central extension $\mathcal{Z}$). The anticommutation relation of the two different supercharges is given as:
$$\{Q^...
- 199
6
votes
3
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Is there an anticommutator relation for orbital angular momentum?
So I know that there are commutator relations for $L$ such as $[L_x,L_y] = i\hbar L_z$, but is there a relation for the anticommutator? For example, $L_xL_y + L_yL_x$?
- 435
1
vote
2
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How to prove the translation generator commutes with the spinors in SUSY algebra?
I was reading Modern Supersymmetry by John Terning, the book starts with SUSY algebra and says
$$
\left[ P_{\mu} , Q_{\alpha} \right] = \left[ P_{\mu} , Q_{\alpha}^{\dagger} \right] = 0
$$
I am ...
- 247
0
votes
0
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215
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Anti-commutator version of Zassenhaus formula
The Zassenhaus formula goes like
$$
e^{t(X+Y)}= e^{tX}~ e^{tY} ~e^{-\frac{t^2}{2} [X,Y]} ~
e^{\frac{t^3}{6}(2[Y,[X,Y]]+ [X,[X,Y]] )} ~
e^{\frac{-t^4}{24}([[[X,Y],X],X] + 3[[[X,Y],X],Y] + 3[[[X,Y],Y],...
- 4,336
15
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3
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The anticommutator of $SU(N)$ generators
For the Hermitian and traceless generators $T^A$ of the fundamental representation of the $SU(N)$ algebra the anticommutator can be written as
$$
\{T^A,T^{B}\} = \frac{1}{d}\delta^{AB}\cdot1\!\!1_{d} +...
- 609