Understanding Halzen Martin's Use of J_em and J_Y in SU(2)*U(1) Theory

[Neitrino]

Dear All,
I don't understand how/why Halzen Martin use J_em J_3 and introduced J_Y currents to build SU(2)*U(1) theory...can anyone advise something...

thank you

 

[Angryphysicist]

I would suspect perhaps because these are the Casimir operators of the group? Just a wild guess, I don't have a copy of Halzen Martin's book or work or am I able to find a relevant quote :(

 

[sir-pinski]

Halzen and Martin's use of J_em and J_Y in SU(2)*U(1) theory is based on the concept of gauge symmetry and electromagnetic interactions. In this theory, the electromagnetic and weak interactions are unified into a single electroweak force, described by the SU(2)*U(1) gauge group. The J_em and J_Y currents represent the electromagnetic and weak currents, respectively, which are fundamental to understanding the behavior of particles under these interactions.

The J_em current, also known as the electromagnetic current, is associated with the electromagnetic force and is responsible for the interactions between charged particles. On the other hand, the J_Y current, also known as the weak hypercharge current, is associated with the weak force and is responsible for the interactions between particles with different weak isospin values.

By introducing these currents, Halzen and Martin were able to construct a unified theory that explains both the electromagnetic and weak interactions. This is achieved through the use of gauge symmetry, where the SU(2)*U(1) gauge group determines the behavior of particles under both interactions.

In summary, the use of J_em and J_Y currents in SU(2)*U(1) theory is essential in understanding the unification of electromagnetic and weak interactions and provides a comprehensive explanation of the behavior of particles under these forces. I hope this helps clarify the concept for you.