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Superanalysis (Hardcover, 1999 ed.)
Loot Price: R2,850
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Superanalysis (Hardcover, 1999 ed.)
Series: Mathematics and Its Applications, 470
Expected to ship within 18 - 22 working days
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This work can be recommended as an extensive course in
superanalysis, the theory of functions of commuting and
anticommuting variables. It follows the so-called functional
superanalysis which was developed by J. Schwinger, B. De Witt, A.
Rogers, V.S. Vladimirov and I.V. Volovich, Yu. Kobayashi and S.
Nagamashi, M. Batchelor, U. Buzzo and R. Cianci and the present
author. In this approach, superspace is defined as a set of points
on which commuting and anticommuting coordinates are given. Thus
functional superanalysis is a natural generalization of Newton's
analysis (on real space) and strongly differs from the so-called
algebraic analysis which has no functions of superpoints, and where
functions' are just elements of Grassmann algebras. This volume is
important for quantum physics in that it offers the possibility of
extending the notion of space, and of operating on spaces which are
described by noncommuting coordinates. These supercoordinates,
which are described by an infinite number of ordinary real, complex
or p-adic coordinates, are interpreted as creation or annihilation
operators of quantum field theory. Subjects treated include
differential calculus, including Cauchy-Riemann conditions, on
superspaces over supercommutative Banach and topological
superalgebras; integral calculus, including integration of
differential forms; theory of distributions and linear partial
differential equations with constant coefficients; calculus of
pseudo-differential operators; analysis on infinite-dimensional
superspaces over supercommutative Banach and topological
supermodules; infinite-dimensional superdistributions and Feynman
integrals with applications to superfield theory;
noncommutativeprobabilities (central limit theorem); and
non-Archimedean superanalysis. Audience: This volume will be of
interest to researchers and postgraduate students whose work
involves functional analysis, Feynman integration and distribution
theory on infinite-dimensional (super)spaces and its applications
to quantum physics, supersymmetry, superfield theory and
supergravity.
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