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Differential Geometry Through Supersymmetric Glasses (Hardcover)
Loot Price: R2,992
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Differential Geometry Through Supersymmetric Glasses (Hardcover)
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Back in 1982, Edward Witten noticed that classical problems of
differential geometry and differential topology such as the de Rham
complex and Morse theory can be described in a very simple and
transparent way using the language of supersymmetric quantum
mechanics. Since then, many research papers have been written on
this subject. Unfortunately not all the results in this field known
to mathematicians have obtained a transparent physical
interpretation, even if this new physical technique has also
allowed many mathematical results to be derived which are
completely new, in particular, hyper-Kaehler and the so-called HKT
geometry. But in almost 40 years, no comprehensive monograph has
appeared on this subject. So this book written by an expert in
supersymmetric quantum field theories, supersymmetric quantum
mechanics and its geometrical applications, addresses this yearning
gap.It comprises three parts: The first, GEOMETRY, gives basic
information on the geometry of real, complex, hyper-Kaehler and HKT
manifolds, and is principally addressed to the physicist. The
second part 'PHYSICS' presents information on classical mechanics
with ordinary and Grassmann dynamics variables. Besides, the author
introduces supersymmetry and dwells in particular on the
representation of supersymmetry algebra in superspace. And the last
and most important part of the book 'SYNTHESIS', is where the ideas
borrowed from physics are used to study purely mathematical
phenomena.
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