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.
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.
發表於2024-11-28
Gauge Fields, Knots, and Gravity 2024 pdf epub mobi 電子書 下載
這本好書一直沒有書評,小弟我就拋磚引玉吧。 昨天從卓越入手的,今天讀到第三章。書的字體和紙張有點像小說。行文娓娓道來,解釋清晰明瞭。由於作者的用意在於引導,而不是完整嚴格地處理全部內容,所以詳略非常閤像我這種偏物理不好純數學的讀者的胃口,沒有必要繁復證明地地...
評分這本好書一直沒有書評,小弟我就拋磚引玉吧。 昨天從卓越入手的,今天讀到第三章。書的字體和紙張有點像小說。行文娓娓道來,解釋清晰明瞭。由於作者的用意在於引導,而不是完整嚴格地處理全部內容,所以詳略非常閤像我這種偏物理不好純數學的讀者的胃口,沒有必要繁復證明地地...
評分這本好書一直沒有書評,小弟我就拋磚引玉吧。 昨天從卓越入手的,今天讀到第三章。書的字體和紙張有點像小說。行文娓娓道來,解釋清晰明瞭。由於作者的用意在於引導,而不是完整嚴格地處理全部內容,所以詳略非常閤像我這種偏物理不好純數學的讀者的胃口,沒有必要繁復證明地地...
評分這本好書一直沒有書評,小弟我就拋磚引玉吧。 昨天從卓越入手的,今天讀到第三章。書的字體和紙張有點像小說。行文娓娓道來,解釋清晰明瞭。由於作者的用意在於引導,而不是完整嚴格地處理全部內容,所以詳略非常閤像我這種偏物理不好純數學的讀者的胃口,沒有必要繁復證明地地...
評分這本好書一直沒有書評,小弟我就拋磚引玉吧。 昨天從卓越入手的,今天讀到第三章。書的字體和紙張有點像小說。行文娓娓道來,解釋清晰明瞭。由於作者的用意在於引導,而不是完整嚴格地處理全部內容,所以詳略非常閤像我這種偏物理不好純數學的讀者的胃口,沒有必要繁復證明地地...
圖書標籤: 數學 物理 數學物理 規範場 Physics 物理-量子場論 科普 物理-QuantumGravity
對於一個沒學過物理的數學人來說,這本半科普的教材是規範場及Jones-Witten不變量相關問題的比較不錯的導引。當然,看完瞭你也不會明白怎麼數學上嚴格構造Witten不變量。。。
評分想瞭解gauge fields而選瞭這本書,作者試圖更多地從直覺上解釋問題,對於理解挺有幫助的,尤其是Part 1和Part 2的前半部分。但同時也省略瞭嚴格的數學證明。比較有意思的是第一次見到書中定義vector fields的方法,和微分幾何中常見的用section來定義不同。從Maxwell方程到Yang-Mills這部分都很好,但Part 2.5對於link和knots的介紹令人費解,幾何性質與物理意義講得都不清楚;Part 3關於gravity則更是簡略。
評分對於一個沒學過物理的數學人來說,這本半科普的教材是規範場及Jones-Witten不變量相關問題的比較不錯的導引。當然,看完瞭你也不會明白怎麼數學上嚴格構造Witten不變量。。。
評分還不錯
評分還不錯
Gauge Fields, Knots, and Gravity 2024 pdf epub mobi 電子書 下載