Recent content by spin_100

Thank you so much now It all makes sense. Could you recommend a good book on representation theory with applications in physics? I am reading Michael Tinkham's book now.

Could you please explain how it follows from that? Thanks

So in general it is not possible to convert a matrix in ##\operatorname{GL}(n)## to an equivalent unitary matrix by a similarity transformation ?

Sorry, I didn't mention that I am talking about finite-dimensional representation of finite groups. My confusion is how can I convert a matrix representation of a group element with a modulus of determinant not equal to 1 to a similarity transformation? Or does this mean that we can't do it...

So that would mean we can only represent finite groups with matrices whose det have unit modulus. Am i right? I also looked up Zee's group theory in a nutshell. The author states that the matrix representation of group G belongs to the General Linear group and then goes on to prove the...

But that would still mean that the ##|det(A)| = 1##to begin with as similarity transformations on A won't change ##|det(A)|##.

It's about representing groups using matrices and their applications. The author hasn't mentioned anything about the form the matrix representation of the group takes.

So that means all group representations must have det = 1 (should belong to SL(n))?

In Michael Tinkham's book, Group theory and Quantum Physics, he derives a theorem that any matrix representation can be converted to an equivalent transformation which is unitary. i.e ##A## is converted to ## B = S^-1 A S ## such that B is unitary. My question is how is it possible to find such...

Please provide a reference where such a method is discussed.

I am considering a simple problem of a sphere of isotropic dielectric media (permittivity ## \epsilon ## and Radius ##R##) placed in a uniform electric field ## E_0 ## (z-direction). The problem is from Griffiths Chapter 4, example 7. Since, it is a linear dielectric material, ## D = \epsilon E...

This is from Callen's thermodynamics. What does the differentiation with respect to T means for an inexact differential like dQ. Also why is T treated as a constant if we start by replacing dQ by TdS? Any references to the relevant mathematics will be much appreciated.

Also why do we choose the generators to satisfy the commutation relations? I am not able to relate it with rotation? It seems natural for 3D but not sure about Spin -1/2 particles

Thanks. That clears a lot of things for me. So generators of SU(2) in all representations of SU(2) follow the commutation relations, i.e [J_1 , J_2 ] = ih J_3 ? Also could you recommend a beginner book for learning more about this? I have studied abstract algebra. Are there any other prerequisites?

Spin 1/2 particles are two states system in C^2 and so it is natural for the rotations to be described by SU(2), for three states systems like spin - 1 particle, Why do we still use SU(2) and not SU(3) to describe the rotations? Is it possible to derive them without resorting to the eigenvalue...