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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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 <tabbox Abstract> ​ <tabbox 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
  
- <​blockquote>​ +----
-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>​+
  
  
advanced_tools/group_theory.txt · Last modified: 2020/09/07 05:18 by 14.161.7.200