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Representation theory, the subject of the submitted article, is also at the core of our understanding of the particle zoo in physics. A tutorial aimed at mathem
by IngoBlechschmid 6y ago
Representation theory, the subject of the submitted article, is also at the core of our understanding of the particle zoo in physics. A tutorial aimed at mathematicians is here:
John Baez, John Huerta. The Algebra of Grand Unified Theories. https://arxiv.org/abs/0904.1556 https://arxiv.org/abs/0904.1556
- benrbray 6y agoGreat link, thanks! I alway enjoy reading summaries of other fields written by/for mathematicians, since the assumption of mathematical background allows a lot of fluff to be cut out (compared to, e.g. reading a textbook about physics intended for physics students). For background reading, the notes by Teleman 2005, "Representation Theory" [1] are a good intro to the topic. Learning about representation theory helped me understand the power of thinking about mathematical objects in terms of their action on other objects. Just as representation theory studies group actions on vector spaces, the theory of modules is best described as the study of ring actions on commutative groups. Many things happen to be rings (e.g. endomorphism rings of functions, where addition=pointwise addition and multiplication=composition), and modules allow us to apply (almost all of) vector space theory to better understand ring-like objects. [1] https://math.berkeley.edu/~teleman/math/RepThry.pdf https://math.berkeley.edu/~teleman/math/RepThry.pdf [2] Another favorite from John Baez: https://groups.google.com/d/msg/sci.physics.research/aiMUJrOjE8A/jGy2N3IaajwJ https://groups.google.com/d/msg/sci.physics.research/aiMUJrO...