An introduction to symplectic geometry, Hamilton systems and complex geometry Rainer Schimming Schimming Rainer Institute of physics publishing Szczecin 2002,

An introduction to symplectic geometry, Hamilton systems and complex geometry

Rainer Schimming

Preprint series: Institute of physics publishing Szczecin 2002,

MSC 2000

53D05 Symplectic manifolds, general

Abstract
The aim of the paper is to tell theoretical physicists some important mathematical topics and to be, in this framework, as didactical as possible.
From a modern point of view, a great deal of physics - parts of mechanics as well as of field theory - turns out to be a kind of differential geometry, namely {\it symplectic geometry} or, slightly more generally, {\it Poisson geometry}. {\it Hamilton systems} are described in terms of this scheme. Geometry is the true nature of the "canonical formalism" in mechanics and field theory. {\it Complex geometry} and {\it almost complex geometry} are close in spirit to symplectic geometry. Moreover, these kinds of geometries became important in Yang-Mills theory, string theory and other areas of theoretical physics. For these reasons, we introduce into Poisson geometry, symplectic geometry, Hamilton systems, almost complex geometry, and complex geometry in one text.
The reader is supposed to know fundamentals of linear algebra, analytic geometry, and differential geometry.


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