Topological Quantum Field Theories: Relations between Knot Theory and Four Manifold Theory

  • B. Grossman
Part of the NATO ASI Series book series (NSSB, volume 245)


We discuss Topological Quantum Field Theories related to the Donaldson theory of four manifolds through dimensional reduction. This leads to theories of instantons, magnetic monopoles, vortices as well as other theories. Stochastic quantization offers a unifying picture of relating theories differing in one dimension. We show how the different topological field theories offer different perspectives on knot theory. Finally, a four-dimenensional picture of surfaces in four dimensions is proposed as a four manifold viewpoint on knot theory.


Modulus Space Riemann Surface Wilson Loop Topological Charge Conformal Field Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • B. Grossman
    • 1
  1. 1.Rockefeller UniversityN.Y.USA

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