This shows you the differences between two versions of the page.
Both sides previous revision Previous revision | Next revision Both sides next revision | ||
advanced_tools:group_theory [2018/04/08 17:15] georgefarr ↷ Links adapted because of a move operation |
advanced_tools:group_theory [2018/04/13 09:42] bogumilvidovic [Why is it interesting?] |
||
---|---|---|---|
Line 195: | Line 195: | ||
<blockquote>A man who is tired of group theory is a man who is tired of life. <cite> Sidney Coleman</cite></blockquote> | <blockquote>A man who is tired of group theory is a man who is tired of life. <cite> Sidney Coleman</cite></blockquote> | ||
+ | <blockquote>Group theory is, in short, the mathematics of symmetries. You already know that | ||
+ | symmetries can be very important in understanding or simplifying physics problems. | ||
+ | When you study classical mechanics, you learn that symmetries of a system | ||
+ | are intimately related to the existence of conserved charges. Their existence often | ||
+ | makes solving for the dynamics a lot simpler. Even if a symmetry is not present | ||
+ | exactly (for instance, when a system is almost-but-not-quite spherically symmetric), | ||
+ | we can often describe the system as a small perturbation of a system that does | ||
+ | exhibit symmetry. A surprisingly large number of physics problems is built around | ||
+ | that idea; in fact, practically all systems for which we can solve the dynamics exactly | ||
+ | exhibit some sort of symmetry that allow us to reduce the often horrible secondorder | ||
+ | equations of motion to much simpler first-order conservation equations.<cite>http://maths.dur.ac.uk/users/kasper.peeters/pdf/groups.pdf</cite></blockquote> | ||
<tabbox Overview> | <tabbox Overview> |