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advanced_tools:group_theory [2018/03/28 16:24] jakobadmin |
advanced_tools:group_theory [2018/03/28 16:25] jakobadmin [Abstract] |
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* One of the best books to get familiar with many of the most important advanced topics in group theory is "Geometrical methods of mathematical physics" by Bernard F. Schutz | * One of the best books to get familiar with many of the most important advanced topics in group theory is "Geometrical methods of mathematical physics" by Bernard F. Schutz | ||
* Other nice advanced textbooks are: | * Other nice advanced textbooks are: | ||
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* J. Frank Adams, Lectures on Lie Groups | * J. Frank Adams, Lectures on Lie Groups | ||
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- | Consider two descriptions of the same phenomenon: (1) Space is homogeneousand isotropic. (2) Space is invariant under translations and rotations of coor-dinates. Statements in the logical form of (1) were exclusive in pre-twentiethcentury physics. Statements in the form -of (2) dominate twentieth centuryphysics; quantum mechanics contains various representations of the same phy-sical state and rules for transforming among them. Description (1) appearsclean; it describes nature without explicit conventional and experientialnotions. Description (2) is all contaminated; it invokes conventional coordi-nates and intellectual transformations of the coordinates. The coordinates areusually interpreted as perspectives of observations; so they are somehowrelated to human subjects. However, physicists agree that (2) is more objective,for it uncovers the hidden presuppositions of (1) and neutralizes their undesir-able effects. They retrofit the conceptual structure embodied in (2) into classi-cal mechanics to make it more satisfactory. The statement (1) is often interpreted in a framework of things; (2) can beinterpreted in the framework of objects. The object framework includes thething framework as a substructure and further conveys the epistemological ideathat the things are knowable through observations and yet independent ofobservations. The two frameworks exemplify two different views of the world | + | |
- | <cite>From "How is Quantum Field Theory possible" by Auyang</cite> | + | |
- | </blockquote> | + | |