規(guī)范場、紐結(jié)和引力

前言

Two of the most exciting developments of 20th century physics weregeneral relativity and quantum theory，the latter culminating in the'standard model'of particle interactions．General relativity treats grav-jty，while the standard model treats the rest of the forces of nature．Unfortunately,the two theories have not yet been assembled into asingle coherent picture of the world．In particular，we do not havea working theory of gravity that takes quantum theory into account．Attempting to'quantize gravity'has led to many fascinating develop-ments in mathematics and physics,but it remains a challenge for the21st century．The early 1980s were a time of tremendous optimism concerningstring theory．This theory was very ambitious,taking as its guidingphilosophy the idea that gravity could be quantized only by unilying itwith all the other forces．As the theory became immersed in ever morecomplicated technical issues without any sign of an immediate payoff intestable experimental predictions，some of this enthusiasm diminishedamong physicists．Ironically，at the same time，mathematicians foundstring theory an ever more fertile source of new ideas．A particularlyappealing development to mathematicians Was the discovery by Ed-ward Witten in the late 1980s that Chern-Simons theory-a quantumfield theory in 3 dimensions that arose as a spin一off of string theory-Was intimately related to the invariants of knots and links that hadrecently been discovered by Vaughan Jones and others．Quantum fieldtheory and 3-dimensional topology have become firmly bound togetherever since，although there iS much that remains mysterious about therelationship．

內(nèi)容概要

The Series on Knots and Everything: is a book series polarized around the theory of knots. Volume 1 in the series is Louis H Kanffman's Knots and Physics.　　One purpose of this series is to continue the exploration of many of the themes indicated in Volume 1. These themes reach out beyond knot theory into physics, mathematics, logic, linguistics, philosophy, biology and practical experience. All of these outreaches have relations with knot theory when knot theory is regarded as a pivot or meeting place for apparently separate ideas. Knots act as such a pivotal place.We do not fully understand why this is so. The series represents stages in the exploration of this nexus.

作者簡介

作者：(美國)約翰貝茲 (Baez.J.)

書籍目錄

PrefaceI  Electromagnetism 1  Maxwell's Equations 2 Manifolds 3 Vector Fields 4 Differential Forms 5  Rewriting Maxwell's Equations 6 DeRham Theory in Electromagnetism Notes to Part III  Gauge Fields 1 Symmetry 2 Bundles and Connections 3  Curvature and the Yang-Mills Equation 4 Chern-Simons Theory 5  Link Invariants from Gauge Theory Notes to Part IIIII  Gravity 1  Semi-Riemannian Geometry 2  Einstein's Equation 3  Lagrangians for General Relativity  4  The ADM Formalism 5  The New VariablesNotes to Part IIIIndex

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