5 votes
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$6j$-symbol example in Quantum Mechanics

It is a shame that most articles about $6j$-symbols (including Wikipedia) fail to mention for what they are actually used. They are used to transform between different coupling schemes in systems with ...
Thomas Fritsch's user avatar
4 votes
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Projector onto Adjoint and Singlet Representations for $SU(N)$

Indeed. Review for su(2), in your notation, where $\vec S$ are the normalized 3-vector generators, so $\vec \sigma /2$ for the fundamental and anti fundamental, so you have $$ \vec{S}_1\cdot \vec{S}_2=...
Cosmas Zachos's user avatar
2 votes

Degrees of freedom in $(A,B)$ representation of the Lorentz group

Now since this is a direct sum of a $2A+1$ dimensional representation with a $2B+1$ dimensional representation, the matrix representation of $(A,B)$ is $2A+2B+2$ dimensional, which is what I would ...
Cosmas Zachos's user avatar
2 votes
Accepted

Addition of angular momenta with relative coefficients

Well, assuming these represent rotation of a tensor product space, so operators of different subscripts commute, and they satisfy the rotation group Lie algebra, $$ [J^a_i,J^b_j]=i\epsilon^{abc} J^c_i ...
Cosmas Zachos's user avatar
1 vote

Character Table and Binary Basis

The final column is obtained by representing the abstract group as an isometry subgroup. Each set of quadratic polynomials (separated by a semicolon) span an irreducible representation whose type is ...
LPZ's user avatar
  • 10.9k
1 vote
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Unitary representation of physics groups in Wu-Ki Tung book

Indeed, the author illustrates by explicit construction that, for noncompact groups (contrast to what you have learned in SO(3) !), their unitary representations (Hermitian irreps for the generators) ...
Cosmas Zachos's user avatar
1 vote

In what sense are fields representations of the Poincare group?

Fields are reducible representations (by which I mean, fields are elements of the vector space on which a reducible representation of the Poincar'e group acts). On the other hand, particles are ...
Prahar's user avatar
  • 25.5k

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