Group Theory & Physics (1): Definitionspic.twitter.com/wCxbvRr4BY
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Group Theory & Physics (2): Example and Intuition The set of all n x n matrices does 𝒏𝒐𝒕 form a group, but the set of n x n 𝒊𝒏𝒗𝒆𝒓𝒕𝒊𝒃𝒍𝒆 matrices does. This group is known as the General Linear Group, denoted GL(n).pic.twitter.com/9nqMVWPKgH
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Group Theory & Physics (2b): Example & Intuition One last intuition before moving on to the fun stuff..pic.twitter.com/6w7W0daMQy
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Group Theory & Physics (3): Lie Groups The defining property of a Lie Group is that the group elements can be parametrized by a continuous variable.pic.twitter.com/pNJd0n5VRj
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Group Theory & Physics (4): Lie Groups SU(2) & SO(3) These are two of the most important groups in physics, and are at the heart of Quantum Mechanics, Special Relativity, and Quantum Field Theory.pic.twitter.com/axBTNurgJX
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All the content of this thread can now also be found on my website here: https://sites.uci.edu/inertialobserver/mathematics-for-physics/ …
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Besides the more mathematical approach (& differential geometry) of e.g. Bröcker and Tom Dieck: https://www.springer.com/gp/book/9783540136781 … The following are very good reads for physicists: https://www.amazon.com/s?k=9780817647148&i=stripbooks&linkCode=qs&tag=physicstoday-20 … (by Nadir Jeevanjee) & Robert Gillmore: Lie Groups, Physics and Geometry. Excellent!pic.twitter.com/zXRwrbO2xL
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