I am struggling with the definition of a unification. I read this question and i am wondering why the standard model is not unifying strong and weak force according to the given definition of a unification, namely that "'Unification' refers to explaining two sets of phenomena (theories) which were previously unrelated, and combining them into a single cohesive description."
Isn't the Standard Model exactly doing this with all three forces? It gives a frame (even in one lagrangian) that explains all three forces.
Regarding to this question I am wondering what we mean when we say the lagrangian of the SM is $SU(3)\times SU(2)\times U(1)$ invariant. In my understanding there is a part which is $SU(3)$ invariant and a part that is $SU(2)\times U(1)$ invariant.
So my questions are:
- What is the precise definition of a unification in QFT?
- Why is the standard model not a unified theory for the strong and electroweak forces (and why is it for the electroweak theory?)
- In which sense is the SM-lagrangian $SU(3)\times SU(2)\times U(1)$ invariant? Or alternatively in which sense is it invariant if we define the charge of each field under each specific group?