The group-representations tag has no wiki summary.
3
votes
1answer
718 views
How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?
This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell (I'm reading this for fun- it isn't a homework problem.)
Show, by explicit calculation, that ...
3
votes
2answers
415 views
How does non-Abelian gauge symmetry imply the quantization of the corresponding charges?
I read an unjustified treatment in a book, saying that in QED charge an not quantized by the gauge symmetry principle (which totally clear for me: Q the generator of $U(1)$ can be anything in ...
10
votes
3answers
835 views
Adding 3 electron spins
I've learned how to add two 1/2-spins, which you can do with C-G-coefficients. There are 4 states (one singlet, three triplet states). States are symmetric or antisymmetric and the quantum numbers ...
2
votes
3answers
324 views
Spin decomposition in general
I can turn-the-crank and show that $\frac{1}{2}\otimes \frac{1}{2} = 1\oplus 0$ etc, but what would be a strategy to proving the general statement for spin representations that $j\otimes s ...
7
votes
2answers
613 views
Why is the string theory graviton spin-2?
In string theory, the first excited level of the bosonic string can be decomposed into irreducible representations of the transverse rotation group, $SO(D-2)$. We then claim that the symmetric ...
2
votes
0answers
249 views
composition of space expansion and movement as a gauge invariance
suppose i have a space-time where we have one point-like object* which we will call movement space probe or $\mathbf{M}_{A}$ for short, and it will be moving with constant velocity $V^A_{\mu}$ in ...
10
votes
2answers
518 views
Is the G2 Lie algebra useful for anything?
Seems like all the simpler Lie algebras have a use in one or another branch of theoretical physics. Even the exceptional E8 comes up in string theory. But G2? I've always wondered about that one. ...
7
votes
1answer
561 views
Representation of the Galileo Group and Central Charges
I've arrived at this question because I've been reading Weinberg's Quantum Theory of Fields Volume I, and I'm in the second chapter about relativistic quantum mechanics. Weinberg discusses the ...
5
votes
1answer
218 views
Identification of the state of particle types with representations of Poincare group
In the second chapter of the first volume of his books on QFT, Weinberg writes in the last paragraph of page 63:
In general, it may be possible by using suitable linear combinations of the ...
6
votes
1answer
402 views
Modes of a QFT and irreducible representation of the gauge group
This is in reference to the calculation in section 3.3 starting page 20 of this paper.
I came across an argument which seems to say that the "constraint of Gauss's law" enforces gauge theory on ...
7
votes
2answers
323 views
Groups acting on physics - a clarification on electrons and spin
My first question is fairly basic, but I would like to clarify my understanding. The second question is to turn this into something worth answering.
Consider a relativistic electron, described by a ...
5
votes
2answers
186 views
If the S-matrix has symmetry group G, must the fields be representations of G?
If the fields in QFT are representations of the Poincare group (or generally speaking the symmetry group of interest), then I think it's a straight forward consequence that the matrix elements and ...
3
votes
1answer
420 views
Introduction to Physical Content from Adjoint Representations
In particle Physics it's usual to write the physical content of a Theory in adjoint representations of the Gauge group. For example:
$24\rightarrow (8,1)_0\oplus (1,3)_0\oplus (1,1)_0\oplus ...
1
vote
0answers
62 views
What is an isoscalar factor?
I need to find a definition for "the isoscalar factors of 3j-symbols for the restriction $SO(n)\supset SO(n-1)$...denoted by brackets with a composite subscript $(n: n-1)$..." They are given as:
$$
...
2
votes
1answer
71 views
Charge of a field under the action of a group
What does it mean for a field (say, $\phi$) to have a charge (say, $Q$) under the action of a group (say, $U(1)$)?
