is there anyone have knowledge about group theory?

Question

lena772 · Answer

Quantum mechanics showed that the elementary systems that matter is made of, such as electrons and protons, are truly identical, not just very similar, so that symmetry in their arrangement is exact, not approximate as in the macroscopic world. Systems were also seen to be described by functions of position that are subject to the usual symmetry operations of rotation and reflection, as well as to others not so easily described in concrete terms, such as the exchange of identical particles. Elementary particles were observed to reflect symmetry properties in more esoteric spaces. In all these cases, symmetry can be expressed by certain operations on the systems concerned, which have properties revealed by Group Theory, a rather obscure branch of mathematics that had previously been mainly a curiosity without practical application.

Physics uses that part of Group Theory known as the theory of representations, in which matrices acting on the members of a vector space is the central theme. It allows certain members of the space to be created that are symmetrical, and which can be classified by their symmetry. It is found that all the observed spectroscopic states of atoms and molecules correspond to such symmetrical functions, and can be classified accordingly. Among other things, it gives selection rules that specify which transitions are observed, and which are not. These matters are so commonplace in spectroscopy that the fact that they are extraordinary and wonderful is hardly realized.

anonymous · Answer

i mean that i have a problem about group theory if someone have knowledge about it..  i know what is the group theory and how to be used by physicist. Thank you anyway.

lena772 · Answer

Ok. Sorry I couldn't help.

anonymous · Answer

I mean, you're welcome to ask the question and then see if anyone can answer it.

anonymous · Answer

it is about invariant subgroup. 

S3 is permutation group

proof this.. 

N= Ce + Ca 

G=S3= N + Nb 

i did something but i think it does not look right..