Representation theory Definition and 67 Threads

For some reason, diffeomorphism invariance seems to be treated like a second-class citizen in the land of symmetries. In nonrelativistic quantum mechanics, we consider Galilean invariance so important that we form our Hilbert space operators from irreducible representations of the Galilei...

I am familiar with the representation theory of finite groups and Lie groups/algebra from the mathematical perspective, and I am wondering how quantum mechanics/quantum field theory uses concepts from representation theory. I have seen the theory of angular momentum in quantum mechanics, and I...

Hi, I am currently studying Lie Algebra in Particle Physics' by Howard Georgi. I am finding the notes on Weights and Roots quite confusing. Can anyone suggest another book which explains this bit in a better fashion?

Homework Statement Hey, this is problem 4A out of Georgi (Lie Algebras in particle physics). The question says given an operator O_x , x=1,2, in the spin 1/2 rep of SU(2). [J_a,O_x]=O_y(\sigma_a)_{yx}/2 where \sigma_a are the Pauli spin matrices. Given A=\langle 3/2, -1/2...

I have only very little knowledge of group theory and representation theory. There is a lot to learn, so I wondered what are the final contributions to physical understanding from representation theory? I'd like to find some less abstract results. For example that the mass is the Casimir...

What's the use of it? Anyone show a simple but illustrative example of the usefulness of representation theory? I can see how faithful representations might be useful but not fully. What I can't imagine is how unfaithful representations can be of any use. Thanks

Hi, I'm reading about Gelfand's representation theory for Banach algebras and I have a small problem with one of the proofs. Let A be a commutative Banach algebra with unit, define \Gamma_A=\left\{\varphi:A\to\mathbb{C}:\varphi\neq0, \varphi \text{ an algebra homomorphism }\right\} to be...

I'm done a basic course on representation theory and character theory of finite groups, mainly over a complex field. When the order of the group divides the characteristic of the field clearly things are very different. What I'd like to learn about is what happens when the field is not...

I'm trying to derive the Gell Mann matrices for fun, but I really don't know representation theory. Can somebody help me? I have Hall's and Humphrey's books, but only online versions and staring at them makes me go crosseyed, and I'm to broke to buy a real book on representation theory. Let...

Why is there 'combinatorial' in front of both of combinatorial group theory and combinatorial representation theory? What does it imply? What is the difference and similiarities between cgt and crt besides the fact that they both have the word combinatorial in front of them?

What is the connection between the two if any? What kind of algebra would Lie groups be best labeled under?

I am going to ask some general questions about representation theory which may sound stupid as I don't know anything about it. How old or new is this theory? How did it come out? What is the general consensus of ths difficulty of the subject? Are there many open problems in this theory? Is...

Hey guys, I was just wondering if you have a good references to the use of Young diagrams/Tableuxs specifically to deduce the representation theory of various Lie groups *other than SU(N)* I know how it works for SU(N) and those groups that can be split into tensor copies theoreof, but I have...

Hello all, Can anybody help me solve the following exercises from the book: Representation Theory, A first course by William Fulton and Joe Harris,1991 page 138, exercise 10.3 page 140, exercise 10.7 page 141, exercise 10.9 Thanks in Advance,

If I have a faithful nondegenerate representation of a C*-algebra, A: \pi\,:\,A \rightarrow B(\mathcal{H}) where B(\mathcal{H}) is the set of all bounded linear operators on a Hilbert space. And just suppose that a\geq 0 \in A. How is the fact that a is positive got anything to do with...

Has it been done...? If so, any textbook on it...? The concept of Rigged Hilbert Spaces is essential to Quantum Mechanics. Symmetries are implemented in physics by doing representation theory of some symmetry groups, almost all of them being Lie groups: Galilei group, Poincaré group...

I think I will write out the beginnings of a "book" that I'd been meaning to get around to starting at some point. Better that someone might actually read it here than trust to them finding it on my web page. Any requests, let me know by PM (or if this is inappropriate for this forum)...