Structure of Dynamical Systems : Symplectic View of Physics

The aim of this text is to treat all three basic theories of physics (classical, statistical and quantum mechanics) from the same perspective, namely that of symplectic geometry, in order to show the unifing power of the symplectic geometry approach.

The book aims to give the reader an understanding of the interrelationships of the three basic theories of physics.

The first two chapters give the necessary mathematical background in differential geometry, Lie groups, and symplectic geometry.

In chapter three a symplectic description of Galilean and relativistic mechanics is given, culminating in the classification of elementary particles (relativistic and non-relativistic, with or without spin, with or without mass).

In the fourth chapter statistic mechanics is put into symplectic form, finishing with a symplectic description of the kinetic theory of gases and the computation of specific heats.

The final chapter covers the author's theory of geometric quantization, and included in this chapter are the derivations of the various wave equations, and the construction of the Fock space. This text is aimed at graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics and geometric quantization.