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Lecture Notes On Chern-simons-witten Theory (Paperback)
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Lecture Notes On Chern-simons-witten Theory (Paperback)
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This invaluable monograph has arisen in part from E Witten's
lectures on topological quantum field theory in the spring of 1989
at Princeton University. At that time Witten unified several
important mathematical works in terms of quantum field theory, most
notably the Donaldson polynomial, the Gromov-Floer homology and the
Jones polynomials.In his lectures, among other things, Witten
explained his intrinsic three-dimensional construction of Jones
polynomials via Chern-Simons gauge theory. He provided both a
rigorous proof of the geometric quantization of the Chern-Simons
action and a very illuminating view as to how the quantization
arises from quantization of the space of connections. He
constructed a projective flat connection for the Hilbert space
bundle over the space of complex structures, which becomes the
Knizhik-Zamolodchikov equations in a special case. His construction
leads to many beautiful applications, such as the derivation of the
skein relation and the surgery formula for knot invariant, a proof
of Verlinde's formula, and the establishment of a connection with
conformal field theory.In this book, Sen Hu has added material to
provide some of the details left out of Witten's lectures and to
update some new developments. In Chapter 4 he presents a
construction of knot invariant via representation of mapping class
groups based on the work of Moore-Seiberg and Kohno. In Chapter 6
he offers an approach to constructing knot invariant from string
theory and topological sigma models proposed by Witten and Vafa.
The localization principle is a powerful tool to build mathematical
foundations for such cohomological quantum field theories.In
addition, some highly relevant material by S S Chern and E Witten
has been included as appendices for the convenience of readers: (1)
Complex Manifold without Potential Theory by S S Chern, pp148-154.
(2) "Geometric quantization of Chern-Simons gauge theory" by S
Axelrod, S D Pietra and E Witten. (3) "On holomorphic factorization
of WZW and Coset models" by E Witten.
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