advanced_tools:group_theory

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advanced_tools:group_theory [2018/04/08 15:15] georgefarr ↷ Links adapted because of a move operation |
advanced_tools:group_theory [2018/04/13 07:42] (current) bogumilvidovic [Why is it interesting?] |
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<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> |

advanced_tools/group_theory.txt · Last modified: 2018/04/13 07:42 by bogumilvidovic

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