4: GAUGE FIELDS, KNOTS AND GRAVITY (Series on Knots and Everything)
暫譯: 4: 測量場、結與重力（結與一切系列）

John Baez, Javier P Muniain

4: GAUGE FIELDS, KNOTS AND GRAVITY (Series on Knots and Everything)
  • 出版商: World Scientific Pub
  • 出版日期: 1994-10-11
  • 售價: $3,140
  • 貴賓價: 9.5 折 $2,983
  • 語言: 英文
  • 頁數: 486
  • 裝訂: Paperback
  • ISBN: 9810220340
  • ISBN-13: 9789810220341
  • 相關分類: 離散數學 Discrete-mathematics

    • 下單後立即進貨 (約2~4週)

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商品描述

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.

商品描述(中文翻譯)

這是一本介紹理解結理論與量子重力之間關係所需的基本數學工具的書籍。書中首先快速介紹了流形（manifolds）和微分形式（differential forms），強調這些工具如何提供一種適當的語言來在任意時空上表述麥克斯韋方程（Maxwell's equations）。接著，作者介紹了向量束（vector bundles）、聯絡（connections）和曲率（curvature），以便將麥克斯韋理論推廣到楊-米爾斯方程（Yang-Mills equations）。書中簡要描述了規範理論（gauge theory）與新發現的結不變量（knot invariants），例如瓊斯多項式（Jones polynomial）之間的關係。然後引入黎曼幾何（Riemannian geometry），以描述愛因斯坦的廣義相對論方程（Einstein's equations of general relativity），並展示量子化重力的嘗試如何導致結理論的有趣應用。

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