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Results tagged with group-theory
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user 27415
Group theory is a branch of abstract algebra. A group is a set of objects, together with a binary operation, that satisfies four axioms. The set must be closed under the operation and contain an identity object. Every object in the set must have an inverse, and the operation must be associative. Groups are used in physics to describe symmetry operations of physical systems.
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$C_4$ symmetry of Chern insulator
A rotation about $\hat{n}$ by an angle $\phi$ acts on spins according to $R(\hat{n},\phi) = e^{\frac{\vec{s}\cdot\hat{n}\phi}{i\hbar}}$, where $\vec{s} = \frac{\hbar}{2} \vec{\sigma}$ where, so that, …
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Invariance of angular momentum states to 180 degree rotations
Can it be shown that an angular momentum eigenstate $ | j, 0 \rangle $ with even $j$ is invariant to 180 degree rotations about the y axis (or any axis $\bot$ z)?
I was able to do this using propertie …
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symmetry group of multi-electron atom
Neglecting spin effects, the energy levels of multi-electron atoms are characterized by states of definite total orbital ($L^2$) and spin angular momentum ($S^2$).
From this it seems that the symmetr …
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Projective representations and reduction of half-integer spin representations under $C_{\inf...
Suppose we have an orthonormal basis of states $|j,m,p\rangle$ where
$j=\frac{1}{2},\frac{3}{2},\ldots$ is the angular momentum quantum number associated with some angular momentum operator $\mathbf{ …
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Projective representations and reduction of half-integer spin representations under $C_{\inf...
I have a partial answer to some of the questions posed.
First off, by analyzing the characters of the action of group $G \equiv \{R^z_\phi : \phi \in [0,4\pi)\} \cup \{\Sigma^z_\phi : \phi \in [0,4\pi …
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