# Symmetry groups [closed]

I am quite new to this subject. I am just repeating in a few words, what I have learned so far: There are 4 fundamental forces of nature: strong, weak, electromagnetism and gravity. Physicists are trying to re-generate a condition, a very high temperature during the Big Bang, to find out which force actually works during that time. The Weinberg-Glashow and Abdus Salam model unified weak and electromagnetism to electro-weak force. Gravity still lays undefined in the Standard Model. At Planck's scale, physicists observe that the 4 forces of nature unify to one single force. We have not yet been able to define that force as yet but the quest is on.

Now the U(1), SU(2), SU(3)........What are these? Can anyone please help me understand, sequentially how the theories evolved? The Grand Unified theory is one which is SU(5)? Does SU stand for special unitary group?

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## closed as too broad by Qmechanic♦Sep 18 '13 at 13:18

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

Hi and welcome to Physics.SE! The title of your questions refers to Supersymmetry, but its body makes no reference what so ever to it. Please consider changing the question's title or expanding your question. – Neuneck Sep 9 '13 at 7:18
"to find out which force actually works during that time." all of the forces work all of the time. The question is whether or not the forces we know are different aspects of the same force at high energies. – Michael Brown Sep 9 '13 at 8:37
This question is very broad and Expects a summary of several decades of development in Physics. It would not be easy to communicate the essence in a quick answer. Perhaps You should start reading text books in Physics if you really want to understand what GUT's are all about. Broadly If you understand that the structure of EM follows from the concept of Local Phase invariance of the charged particle fields(The U1 symmetry), Then more generally Gauge theory(SU2, SU3, SU5 and ....) is a generalization of that concept. – Prathyush Sep 9 '13 at 9:41
Does the OP know group theory and linear algebra? If not the answer will be very long indeed, even without answering the request for the steps in development of gauge theory. Book recommendations may be more appropriate. – Philip Gibbs - inactive Sep 9 '13 at 14:24
Thank you for the reply. Yes, I do understand linear algebra, but what I was trying to understand is that how Standard model is related in this special unitary groups. If anybody can give me a vision? – Shounak Bhattacharya Sep 18 '13 at 11:23

You are right about U(1) and SU(N) referring to the (special) unitary groups. In a quantum field theory they are used to describe gauge interactions. In sucha gauge theory, one demands that the symmetry of the system is local, i.e. you can choose transformation parameters at any spacetime point independently from all others, without physics behaving differently.

Grand Unified Theories in general unify the strong and electroweak interactions only. Gravity is still left out of the game. Theories that incorporate gravity as well are called Theories of Everything (ToE). The $SU(5)$ is one possible realization of a Grand Unified Theory. Other possibilities include $SO(10)$, $E(6)$ or the Pati-Salam model ($SU(4) \times SU(2)_L \times SU(2)_R$, although one could argue whether this is unified, as it still is no simple gauge group).

I can not give a historical account on how gauge theories and the Standard Model as well as the Grand Unified Idea evolved, but Wikipedia might have some pointers for you.

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