Difference between revisions of "Literature on Symmetry"
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[[Symmetry|Symmetries]] can be studied by [[group]]s and [[action]]s (or [[operator]]s) applied to it. Note that these three terms are represented in plural form. The ability to count the number of symmetries or explicitly distinguish the consequences of actions in sequences and in combinations are the [[Concept|core concept]]s of symmetry studies. Symmetry is one critical property of being [[Equivalent]]<ref>{{:Paper/General Theory of Natural Equivalences}}</ref>, and is directly linked with Adjoint Functors, a.k.a. [[Galois Connections]]. [[Brendan Fong]] also discuss the notion of [[symmetry]] in his doctoral thesis<ref>{{:Thesis/The Algebra of Open and Interconnected Systems}}</ref>. | [[Symmetry|Symmetries]] can be studied by [[group]]s and [[action]]s (or [[operator]]s) applied to it. The foundational ideas of symmetries came from [[Emmy Noether]] and here paper:[[Paper/Invariant Variation Problems|Invariant Variation Problems]]<ref>{{:Paper/Invariant Variation Problems}}</ref>. Note that these three terms are represented in plural form. The ability to count the number of symmetries or explicitly distinguish the consequences of actions in sequences and in combinations are the [[Concept|core concept]]s of symmetry studies. Symmetry is one critical property of being [[Equivalent]]<ref>{{:Paper/General Theory of Natural Equivalences}}</ref>, and is directly linked with Adjoint Functors, a.k.a. [[Galois Connections]]. [[Brendan Fong]] also discuss the notion of [[symmetry]] in his doctoral thesis<ref>{{:Thesis/The Algebra of Open and Interconnected Systems}}</ref>. | ||
=Connection with Least Action and Lagrange Mechanics= | =Connection with Least Action and Lagrange Mechanics= | ||
Latest revision as of 09:59, 31 July 2022
Symmetries can be studied by groups and actions (or operators) applied to it. The foundational ideas of symmetries came from Emmy Noether and here paper:Invariant Variation Problems[1]. Note that these three terms are represented in plural form. The ability to count the number of symmetries or explicitly distinguish the consequences of actions in sequences and in combinations are the core concepts of symmetry studies. Symmetry is one critical property of being Equivalent[2], and is directly linked with Adjoint Functors, a.k.a. Galois Connections. Brendan Fong also discuss the notion of symmetry in his doctoral thesis[3].
Connection with Least Action and Lagrange Mechanics
It would be helpful to learn more about the Principle of Least Action[4][5]and Lagrangian Mechanics after learning the notion of symmetry.
For people who are interested in Symmetry, please watch the video by Group Theory by Gareth Jones on Serious Science[6]. Another reference is the youtuber, Number Cruncher[5]
References
- ↑ Noether, Emmy (1971). Translated by Mort Tavel. "Invariant Variation Problems" (PDF). Transport Theory and Statistical Physics. local page. 1 (3): 186–207. arXiv:physics/0503066free to read. doi:10.1080/00411457108231446. (Original in Gott. Nachr. 1918:235–257)
- ↑ Eilenberg, Samuel; Mac Lane, Saunders. "General Theory of Natural Equivalences". Transactions of the American Mathematical Society (Vol. 58, No. 2 (Sep., 1945), ed.). local page: American Mathematical Society: 231-294.
- ↑ Fong, Brendan (2016). The Algebra of Open and Interconnected Systems (PDF) (Ph.D.). local page: University of Oxford. Retrieved October 15, 2021.
- ↑ Miller, Noah (Aug 9, 2018). The Principle of Least Action. local page: NoahExplainsPhysics.
- ↑ 5.0 5.1 A German math Teacher, ed. (Aug 18, 2021). Physics in 10 minutes - The principle of least action. local page: Mathematics teacher.
- ↑ Jones, Gareth (Jul 9, 2020). Group Theory — Gareth Jones / Serious Science. local page: Serious Science.
