Subatomic rotations in a plane Abelian group

[genloz]

Hi.. I recently stumbled across a question that seemed a little bit odd "Show that the set of rotations in a plane form a SO(2) Abelian group." for a subatomic physics course. I know how to obtain the answer showing that A^TA=AA^T=1... what I don't understand is what the relevance to subatomic physics is and what type of physics process it's modelling...
Thanks!

 

[mormonator_rm]

Hi.. I recently stumbled across a question that seemed a little bit odd "Show that the set of rotations in a plane form a SO(2) Abelian group." for a subatomic physics course. I know how to obtain the answer showing that A^TA=AA^T=1... what I don't understand is what the relevance to subatomic physics is and what type of physics process it's modelling...
Thanks!

just to give a verbal example; neutral meson states, by quark content, fluctuate. The amplitudes of quark content in mesons can be modeled in a unitary matrix that follows the same condition as your example, but has a dimension for each quark type. The amplitudes are related to mixing angles that mix the masses of related mesons in the "mass squared matrix" for a given quantum number.

 

[Norman]

You should take a look at Noether's theorem and the relationship between symmetries of a group and conservation laws.