Topics in Physical Mathematics - ISBN:1848829388

Topics in Physical Mathematics

Date: 21 April 2011, 04:09

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This title adopts the view that physics is the primary driving force behind a number of developments in mathematics. Previously, science and mathematics were part of natural philosophy and many mathematical theories arose as a result of trying to understand natural phenomena. This situation changed at the beginning of last century as science and mathematics diverged. These two fields are collaborating once again; 'Topics in Mathematical Physics' takes the reader through this journey.
The author discusses topics where the interaction of physical and mathematical theories has led to new points of view and new results in mathematics. The area where this is most evident is that of geometric topology of low dimensional manifolds. These include the theories of Donaldson, Chern-Simons, Floer-Fukaya, Seiberg-Witten, and Topological (Quantum) Field Theory.
The author also discusses the interaction of CFT, Supersymmetry, String Theory and Gravity with diverse areas of mathematics. Several of these ideas have led to new insights into old mathematical structures and some have led to surprising new results The term "Physical Mathematics'' has been coined to describe collectively these new and fast growing areas of research, and regards the work of Donaldson and Witten as belonging to this new area of physical mathematics. Study of this work forms an important part of this book.
Content Level » Professional/practitioner
Keywords » classical and quantum field theories - differential geometry and topology - invariants of 3- and 4-dimensional manifolds - physical mathematics
Related subjects » Algebra - Analysis - Geometry & Topology
Contents
Algebra.- Topology.- Manifolds.- Bundles and Connections.- Characteristic Classes.- Theory of Fields, I: Classical.- Theory of Fields, II: Quantum and Topological.- Yang-Mills-Higgs Fields.- 4-Manifold Invariants.- 3-Manifold Invariants.- Knot and Link Invariants.- Dictionary of Terminology.- Historical and Biographical Notes.- Categories and Chain Complexes.- Operator Theory.

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