# Tagged Questions

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### Applications of Algebra in Physics

Often I have heard about the link between Algebra (in particular Representations of Groups and Algebras) and some "indefinite" field of Physics. I have a good preparation in Algebra and ...
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### How we apply representation theory to physics.

I want to have a concrete idea of what people do with representation theory in physics. Here is what I think: Corresponding to a specific "physics", there is particularly a Lie group (called G) of ...
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### Representation theory in physics

0 down vote favorite I'm sorry if this is somewhat a dumb question. First: "Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements ...
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### Closed form for 3j-symbol ratio

I am working on the spherical harmonic decomposition of cosmic microwave background maps, therefore I often deal with functions that are proportional to Wigner 3J symbols/Clebsch Gordan coefficients. ...
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### $SU(2)$ Representation of $SO(3)$

I've often seen it written that $SU(2)$ is a "two-valued representation" of $SO(3)$ (in theoretical physics books mainly). I have a major conceptual issue with this however. I know there is a Lie ...
194 views

### Decomposing products of spinor representations into anti-symmetric tensors

There is always a natural $2^{[\frac{d}{2}]}$ dimensional spinorial representation of $SO(d-1,1)$ (..induced from a representation of the related Clifford algebra..) and if $[m]$ denote the space of ...
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### A particular (functional) determinant calculation

One wants to calculate the quantity, $\det'(\frac{\partial}{\partial t} - i [\alpha, ])$ where the prime on the "det" means that one wants to do a product over only non-zero eigenvalues of the ...
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### Is there a rigorous exposition of 'tensor methods' for finding lie group representations?

I've seen tensor methods in physics for finding lie group representations, as in Wu-Ki Tungs Group Theory in Physics, which uses tensors physics style, ie with indices; and Cvitonovics Birdtracks, ...
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### Does the Casimir depend on normalization of generators?

This question is motivated by something in physics: the area operator in loop quantum gravity is given by the Casimir of $SU(2)$, that is $j(j+1)$ for a dimension $2j+1$ representation of $SU(2)$. I ...
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### Geometric algebra approach to Lorentz group representations

Background: Let $\Lambda$ be the Lorentz transformation parameterized by the asymmetric real matrix $w_{\mu \nu}$. That is, let $\Lambda = \exp(\frac{w_{\mu \nu}}{2}J^{\mu \nu})$, where \$(J^{\mu ...
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### Computation of Clebsch-Gordan cofficients for point groups

In my work I have to deal with space and point groups and their representation. A lot of computations need Clebsch-Gordan coefficients. I am aware of the fact that these coefficients may be found in ...
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### The mathematics behind Clebsch-Gordan Coefficients

In quantum physics we have to work a lot with Clebsch-Gordan coefficients and generalizations like the Wigner 3j,6j, and 9j symbols. In our coursework we are taught that the coefficients are coupling ...
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### What are the differences between classical Yang-Baxter Equation and quantum Yang-Baxter Equation?

what are the differences between classical Yang-Baxter Equation and quantum Yang-Baxter Equation? Thank you very much.
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### Representations of a non-compact group are labeled by its maximal compact subgroup?

I don't have much of any awareness about the representation theory of non-compact Lie groups but I bumped into it for my work. Is there some idea that the representations of a non-compact group are ...
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### Complexifying representations

Let me try to split the question in a few parts, I would like to understand the claim that all non-degenerate bilinear symmetric forms are equivalent over the complex while for the reals they can be ...