This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvat...
This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.
作者简介
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John Carlos Baez is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California. He is known for his work on spin foams in loop quantum gravity. For some time, his research had focused on applications of higher categories to physics and other things.
Baez is also known to science fans as the author ...
John Carlos Baez is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California. He is known for his work on spin foams in loop quantum gravity. For some time, his research had focused on applications of higher categories to physics and other things.
Baez is also known to science fans as the author of This Week's Finds in Mathematical Physics, an irregular column on the internet featuring mathematical exposition and criticism. He started This Week's Finds in 1993 for the Usenet community, and it now has a following in its new form, the blog "Azimuth". This Week's Finds anticipated the concept of a personal weblog. Additionally, Baez is known on the World Wide Web as the author of the crackpot index.
原文摘录
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The naive notion that a particle is a point tracing out a path in spacetime, or that a field assign a number or vector to each point of spacetime, proved to be wholly inadequate, for one cannot measure the position and velocity of a particle simutaneously with arbitrary accuracy, nor the value of a field and its time derivative. (查看原文)
Series on Knots and Everything(共22册)，
这套丛书还有
《Non-Standard Logics and Non-Standard Metrics in Physics》《Virtual Knots》《ALGEBRAIC INVARIANTS OF LINKS》《Orbiting the Moons of Pluto》《New Ideas in Low Dimensional Topology》
等
。
1 有用 嘴阔阔 2019-03-29 15:08:36
好书。日后更新评论。
0 有用 chaosmori 2024-02-14 11:47:03
補
1 有用 xuejiayu 2018-05-02 21:20:51
物理学家学习现代数学优秀教材 2018.5.2 To Part II
1 有用 淇厚生 2017-03-16 17:52:00
对于一个没学过物理的数学人来说，这本半科普的教材是规范场及Jones-Witten不变量相关问题的比较不错的导引。当然，看完了你也不会明白怎么数学上严格构造Witten不变量。。。
2 有用 Egregium 2022-08-15 05:13:48
虽然不是所有人都要去搞高能理论和弦论，但是读一下这本书的前半部分还是很有收获的。作为这个时代的物理系学生，还是应该要对微分几何、拓扑和李群李代数有些基本认识的。
0 有用 chaosmori 2024-02-14 11:47:03
補
2 有用 Egregium 2022-08-15 05:13:48
虽然不是所有人都要去搞高能理论和弦论，但是读一下这本书的前半部分还是很有收获的。作为这个时代的物理系学生，还是应该要对微分几何、拓扑和李群李代数有些基本认识的。
1 有用 嘴阔阔 2019-03-29 15:08:36
好书。日后更新评论。
1 有用 xuejiayu 2018-05-02 21:20:51
物理学家学习现代数学优秀教材 2018.5.2 To Part II
1 有用 淇厚生 2017-03-16 17:52:00
对于一个没学过物理的数学人来说，这本半科普的教材是规范场及Jones-Witten不变量相关问题的比较不错的导引。当然，看完了你也不会明白怎么数学上严格构造Witten不变量。。。