MadSci Network: Physics
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Re: Group Theory and Physics

Date: Fri Jul 24 08:07:10 1998
Posted By: Max Sang, MadSci Admin
Area of science: Physics
ID: 901217267.Ph
Message:

Hi Jonathan

This is not really the place for such complicated discussions - try the newsgroups if you want to take it further. I will give you a flavour of it, though, because it is really beautiful. In my field (particle physics) in the sixties, there was a veritable 'zoo' of short lived particles, generically called hadrons. We knew how they were created and how they decayed in turn, but we didn't have any way of figuring out their internal dynamics (if any). It was tremendously complicated - could nature really be this messy? There were at least 10 different quantum numbers that these things could possess, and different ones were changed in every decay. There was no system for understanding what was going on.

It was known, however, that some of them could be grouped into 'multiplets' of certain types - for instance, if you plotted something called hypercharge against something called isospin, some particles grouped themselves into a lovely little hexagon shape, with two extras in the middle of the hexagon. These eight particles had different masses and decay properties, and most of their other quantum numbers were different too, but they were united in some way by these two numbers into a group of eight, or an 'octuplet'. This was seen by some as very very significant, especially as more and more groupings were being discovered. It turns out that they behave as members of a representation of a particular group. If you do some tricky group decomposition you find that they all come from the same group.

This insight gave birth to modern particle physics - it means we can deduce the group structure of nature BEFORE we know the dynamics. Because of a profound and amazing theorem in mathematics called Noether's theorem, you can prove that, if a system obeys a symmetry (which can be deduced from group theory once you've found the multiplets (ways of grouping particles)) then there must be a special 'conserved' quantity, like electric charge for example. Group theory is so successful (it predicted lots of particles which were found at a later date, predicted quarks, indeed gave rise to most of modern particle physics) that it is now generally believed that the fundamental laws of nature are completely defined by combining a few groups ( SU(3)xSU(2)xU(1), in actual fact ). If (when?) we discover new physics which ISN'T explained by this model, the breakthrough will come from figuring out the new groups.

Well, I can't really dribble on any further, but try reading 'Fearful Symmetry' by A.Zee if your appetite has been whetted. It's not mathematical at all, I promise!
Cheers,
Max


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