What Is the Difference Between Albenian and Nonalbenian in Quantum Field Theory?

[captain]

i am have trouble understanding the difference between these two things and why is nonalbenian used in qft.

 

[Haelfix]

When we talk about abelian groups, it means :

let a, b be elements of a group G. A group is abelian <--> ab = ba.

Groups are constructed and utilized in field theory primarily b/c we notice the laws of nature satisfy certain symmetries called gauge transformations. For instance the U(1) gauge group of electromagnetism is an abelian group and its the simplest example of relevance in the standard model.

Harder to deal with are nonabelian groups where the above property is not satisfied, and there are several examples (like QCD, where the gauge group is SU(3) -color).

 

[captain]

When we talk about abelian groups, it means :

let a, b be elements of a group G. A group is abelian <--> ab = ba.

Groups are constructed and utilized in field theory primarily b/c we notice the laws of nature satisfy certain symmetries called gauge transformations. For instance the U(1) gauge group of electromagnetism is an abelian group and its the simplest example of relevance in the standard model.

Harder to deal with are nonabelian groups where the above property is not satisfied, and there are several examples (like QCD, where the gauge group is SU(3) -color).

can operators be elements of a group?

 

[masudr]

can operators be elements of a group?

The elements of a set with some associated binary operation can be elements of a group if they satisfy the axioms of a group.