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Question from quantum field theory

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From: Krish <krish.tibrewala@gmail.com>
Subject: Quantum field theory

Message Body:
This question relates to the gauge theories behind the strong, weak and electromagnetic forces. A beautiful intertwining of theoretical physics and pure mathematics is when group theory is used to described these forces. For example, the Standard Model of particle physics is perfectly described by: SU(3) x SU(2) x U(1)…..I have enough knowledge in group theory to understand special groups (or at least, understand their conditions) and the unitary group.

However, what I do not understand is how the aforementioned groups even represent the fundamental forces, how they even come into play!

If I had to sum it up, this is my question:

“How is the symmetry SU(2) x U(1) broken? What does it mean for the maths….how is the mathematics adjusted….What does a broken symmetry really MEAN mathematically? How are SU(2), U(1) etc even INVOLVED physically anyways?? Like, how do they represent The weak and electromagnetic forces?”

Thank you very much for your time and help

Asked Krish

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