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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Geometric and Topological Methods for Quantum Field Theory (Paperback, Softcover reprint of hardcover 1st ed. 2005)
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Geometric and Topological Methods for Quantum Field Theory (Paperback, Softcover reprint of hardcover 1st ed. 2005)
Series: Lecture Notes in Physics, 668
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This volume offers an introduction, in the form of four extensive
lectures, to some recent developments in several active topics at
the interface between geometry, topology and quantum field theory.
The first lecture is by Christine Lescop on knot invariants and
configuration spaces, in which a universal finite-type invariant
for knots is constructed as a series of integrals over
configuration spaces. This is followed by the contribution of
Raimar Wulkenhaar on Euclidean quantum field theory from a
statistical point of view. The author also discusses possible
renormalization techniques on noncommutative spaces. The third
lecture is by Anamaria Font and Stefan Theisen on string
compactification with unbroken supersymmetry. The authors show that
this requirement leads to internal spaces of special holonomy and
describe Calabi-Yau manifolds in detail. The last lecture, by
Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer
index theorem and discusses some applications of K-theory to
noncommutative geometry. These lectures notes, which are aimed in
particular at graduate students in physics and mathematics, start
with introductory material before presenting more advanced results.
Each chapter is self-contained and can be read independently.
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