Subatomic rotations in a plane Abelian group

Click For Summary
SUMMARY

The discussion centers on the mathematical concept that the set of rotations in a plane forms a Special Orthogonal Group SO(2), which is an Abelian group. The relevance to subatomic physics is highlighted through the example of neutral meson states, where quark content fluctuations can be modeled using unitary matrices that adhere to similar conditions. The connection between symmetries and conservation laws is emphasized, particularly through Noether's theorem, which is crucial for understanding the implications of these mathematical structures in physical processes.

PREREQUISITES
  • Understanding of Special Orthogonal Groups (SO(2))
  • Familiarity with unitary matrices in quantum mechanics
  • Knowledge of Noether's theorem and its implications in physics
  • Basic concepts of meson states and quark content
NEXT STEPS
  • Study the properties of Special Orthogonal Groups (SO(2)) in detail
  • Explore unitary matrices and their applications in quantum mechanics
  • Investigate Noether's theorem and its relationship to symmetries and conservation laws
  • Research the behavior of meson states and quark mixing in particle physics
USEFUL FOR

This discussion is beneficial for physicists, particularly those specializing in particle physics, quantum mechanics, and theoretical physics, as well as students seeking to understand the mathematical foundations of symmetries in physical systems.

genloz
Messages
72
Reaction score
1
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!
 
Physics news on Phys.org
genloz said:
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.
 
You should take a look at Noether's theorem and the relationship between symmetries of a group and conservation laws.
 

Similar threads

High School Why are SU(3), SU(2) and U(1) groups used in the Standard Model?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Any good idea how non-abelian gauge symmetries emerge?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate What's the relationship between RMS framework and the Lorentz group?
  • · Replies 0 ·
Replies
0
Views
1K
Graduate How to find group types for a particular order?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Free Abelian Groups .... Aluffi Proposition 5.6
  • · Replies 40 ·
2
Replies
40
Views
5K
Graduate Learn SU Groups in QCD: Chiral Symmetry, 8 Goldstone Bosons & More
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad Physical reality of nontrivial loops in SO(3)
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How Does Beta Decay Relate to the Role of W Bosons in Weak Nuclear Force?
  • · Replies 4 ·
Replies
4
Views
5K
Graduate How Does U(1) Double-Cover SO(2) for a Specified Angle?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Showing that a group acts freely and discretely on real plane
  • · Replies 5 ·
Replies
5
Views
2K