Questions tagged [lie-algebra]

A vector space $\mathfrak{g}$ over some field $F$ and kitted with a bilinear, antisymmetric and Jacobi-identity-fulfilling product ("Lie Bracket" or "commutator"). In physics, most often arises as the Lie algebra (tangent space to the identity) of a Lie group; in gauge theories, basis vectors of the gauge group's Lie algebra correspond to Noether currents and conserved quantities.

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Symmetric tensor product decomposition of $su(2)$

Taking the tensor product of two spin 1 representations of $su(2)$ yields $$1 \otimes 1 = 0 \oplus 1 \oplus 2.$$ What changes if instead we take the symmetric tensor product $1 \odot 1$ of these ...
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Highest and Lowest $SU(3)_F$ states

For the finite dimensional $(p,q)$-irreducible representation of $SU(3)_F$, we can label the states as $\mid T_3,Y\rangle$. Where $T_3$ is the third component of isospin and $Y$ is the hypercharge. ...
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Question about angular momentum operator

To show that the eigenvalue to $L^2$ is proportional to $\hbar^2$ is shown from $L_z=xP_y-yP_x$ $p_y=-i\hbar\frac{\partial}{\partial y}$ $p_x=-i\hbar\frac{\partial}{\partial x}$ $L_z=-i\hbar(x\...
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Eigenvalues of Angular Momentum in Quantum Mechanics

The eigenvalue equation of the $L^2$ operator is given by $$L^2f_l^m = \hbar ^2l(l+1)f_l^m$$ Side: So a determinate state for some observable $Q$ is a state where every measurement of $Q$ returns ...
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Derivation of the irreducible representations of SO(3)

Is there a way to derive the representations of $SO(3)$ without the usual method with the ladder operators which also gives the ones of $SU(2)$? The usual way to do these calculations is to start ...

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