I'm just a year 12 student with an interest in mathematics and physics, but I have a question (or rather a few) for particle physicists/mathematicians out there.(adsbygoogle = window.adsbygoogle || []).push({});

I have read a little about abstract algebra - to about the extent of knowing the definition of a group, its relationship to symmetry and such - and I came across the group SU(n), which I understand to have a relationship with the standard model of particle physics with particular values of n. I have read a little on SU(n), enough to find that it is a group of n*n unitary matrices where the determinant is 1. In this sense, first of all, what is a unitary matrix? I understand the concept of a determinant. I also have read that SU(n) has dimension [tex]n^2 - 1[/tex]. I do not follow this argument however. If the group is defined by n*n matrices, how can the group have this number of dimensions?

What is the relationship, if any, between SU(n) and SO(n) - the latter which I understand (if I am not mistaken) to be the group of rotations of n-space about axes through the origin of [tex]\Re^n[/tex] (a fairly abstract but understandable concept)? And how do these concepts explain phenomena in modern particle physics? I believe it is down to symmetry. but, symmetry of what? I understand (but may be far off) that it is "symmetry operations" that create a group, and so, I am asking what these operations are, and what the symmetry itself is.

Also, what do these SU groups relate to within physics in particular? Is it spin/spin angular momentum? Or perhaps colour changes (what are colours in terms of particles)?

Is there any helpful way to visualise these particle physics concepts - with relation to the symmetries - in any simple way, and can the concepts be described well without getting bogged down in difficult mathematics? If so, I'd ask you to, please, have a go.

Sorry for the many questions, but I became very curious recently about this link between what I would have considered before now an obscure (?) branch of mathematics and an exciting field of physics. Thanks in advance for any help in this. :tongue2:

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# Relationship between group theory and particle physics?

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