Subatomic rotations in a plane Abelian group

In summary, the question of showing that the set of rotations in a plane form a SO(2) Abelian group is relevant to subatomic physics as it can be used to model the amplitudes of quark content in mesons. This is similar to Noether's theorem which relates symmetries of a group to conservation laws.
  • #1
genloz
76
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!
 
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  • #2
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.
 
  • #3
You should take a look at Noether's theorem and the relationship between symmetries of a group and conservation laws.
 

1. What is a subatomic rotation?

A subatomic rotation refers to the movement or change in position of a subatomic particle, such as an electron, within an atom. This movement is described by quantum mechanics and can occur in a plane Abelian group, which is a mathematical structure used to study symmetry in physics.

2. What is a plane Abelian group?

A plane Abelian group is a mathematical concept that describes a set of transformations or operations that can be performed on a plane. These transformations maintain the same shape and orientation of the plane, and they follow the principles of commutativity and associativity, which are important in studying symmetry in physics.

3. How are subatomic rotations studied in a plane Abelian group?

In order to study subatomic rotations in a plane Abelian group, scientists use mathematical tools such as group theory and representation theory. These tools allow them to analyze the symmetry of the transformations and make predictions about the behavior of subatomic particles in different situations.

4. What is the significance of studying subatomic rotations in a plane Abelian group?

Studying subatomic rotations in a plane Abelian group is important in understanding the fundamental properties and behavior of subatomic particles. It also helps scientists make predictions about the behavior of matter at a microscopic level, which has practical applications in fields such as material science, chemistry, and technology.

5. How does the concept of subatomic rotations in a plane Abelian group relate to other areas of physics?

The concept of subatomic rotations in a plane Abelian group is closely related to other areas of physics, such as quantum mechanics and particle physics. It is also relevant in fields such as quantum computing, where the manipulation of subatomic particles is used to process information. Additionally, the study of subatomic rotations can provide insights into the fundamental laws of nature and the structure of the universe.

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