Transforming Representations of SO(3) to Act on Vectors?

Thread starter silverwhale
Start date May 16, 2013
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Representations So(3)

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The discussion centers on the representation of the Lie group SO(3) and its action on vectors versus spinors. It clarifies that while the generators of SO(3) can be represented using Pauli matrices, this leads to a representation of SU(2), which is a double cover of SO(3). The 3-dimensional representation of SO(3) is indeed the vector representation, which acts on 3-component vectors, while the spinor representation corresponds to 2-component spinors. The distinction between vector and spinor representations is emphasized, noting that the latter are projective representations that require careful handling in quantum mechanics. Understanding these representations is crucial for applications in quantum field theory and particle physics.

May 18, 2013

silverwhale

dextercioby said:

The truth is that you really need to read mathematics, because explaining the facts without understanding them right now won't help you too much.

The bolded part is incorrect.

I'm not really up to reccomendations to the elementary stuff, i.e. learning something from beginning. I really hate introductory texts and especially on the mathematics behind the physical theory.

I guess saying that:" SU(2) is the double cover of SO(3), and SU(2) is isomorphic to the coset SO(3)/Z2." would have been the right statement although I am not sure what a double cover is.

Introductory texts are the basis, how then would one learn stuff? If not by some "introductory" text that relates to more pedestrian stuff?

Honestly, I do not hate introductory texts about the mathematics of a physical theory, those are the tools one needs to handle the model.. And at the end I want to calculate stuff and get results not just understand some axioms and be happy with it..