# Tagged Questions

Use as a synonym to the representation-theory tag

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### A question about character table of the group Td. Group theory

I am trying to get the character table of the group Td using the basis functions already defined. I have a problem with the basis function (2z^2-x^2-y^2, x^2-y^2) because I don´t get the character -1 ...
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### What is the irreducible decomposition of the tensor product of left and right weyl spinor representations, i.e. $(1/2,0)⊗(0,1/2)$?

What is the irreducible decomposition of the tensor product of left and right weyl spinor representations of the group $SL(2,\mathbb{C})$, i.e. $(1/2,0)⊗(0,1/2)$? I mean, the tensor product of two ...
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### $SU(3)$ structures and branching rules

I am reading this paper http://arxiv.org/abs/hep-th/0211102 and I would like to understand better about the branching rule $SO(6) \equiv SU(4) \rightarrow SU(3)$ used for eq. C.11 in the Appendix. I ...
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### How to manipulate higher spin systems (higher than spin 1/2) using a given operator?

I’ve been reading ¨Halzen, F., and A. D. Martin. Quarks and Leptons. New York: Wiley Text Books, January 1984. ISBN: 9780471887416¨, and I’d like some clarification of a concept, please: I’m ...
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### Why representations instead of just groups?

This question is essentially asking for a clarification on what has already been said in this one. What I don't understand is why it is the representations that are important in Quantum Field Theory ...
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### Rotations in Bloch Sphere about an arbitrary axis

I am trying to understand the following statement. "Suppose a single qubit has a state represented by the Bloch vector $\vec{\lambda}$. Then the effect of the rotation $R_{\hat{n}}(\theta)$ on the ...
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### How is the Lorentz group related to spin? [closed]

I've been reading about the agebra of the Lorentz group. It is given by, $$G\equiv SO(1,3) ~\cong~ SU(2)\times SU^*(2)$$ Now, representations of this group $G$ as labelled by $(j,j')$ where $j$ is ...
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### Symmetry and degeneracy in quantum mechanics

If an operator commutes with the Hamiltonian of a problem, does it always must admit degeneracy? For example, parity operator commutes with the Hamiltonian in case of a free particle and we have two ...
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### Is the local Lorentz transformation a general coordinate transformation?

There is a saying in Nakahara's Geometry, Topology and Physics P371 about principal bundles and associated vector bundles: In general relativity, the right action corresponds to the local Lorentz ...
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### Representation of Lorentz Tranformation on Fields and Wigners theorem

I've been reading about symmetries and I haven't been able piece this information together. I've the Lorentz transformation $$x^\mu \mapsto x^{\rho} = \Lambda_\nu^\mu x^\nu$$ First off, arn't we ...
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### Writing Breit-Pauli spin-spin-coupling Hamiltonian as a sum of irreducible spin tensor operators

The spin-spin interaction part of the Breit-Pauli Hamiltonian for two electrons contains the term 3(\mathbf S_1 \cdot \mathbf r)(\mathbf S_2 \cdot \mathbf r) - r^2 \mathbf S_1 \cdot \...
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### Characters of extra representations in the double group of O

Looking at the character table for $\overline{O}$ (double group of $O$) in a book, I noticed that two out of three of the additional irreps (with respect to the five irreps from $O$ itself) are ...