Physics Through Symmetries

Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.

Develops angular momentum theory in a pedagogically consistent way, starting from the geometrical concept of rotational invariance. Uses modern notation and terminology in an algebraic approach to derivations. Each chapter includes examples of applications of angular momentum theory to subjects of current interest and to demonstrate the connections between various scientific fields which are provided through rotations. Includes Mathematica and C language programs.

Our understanding of the physical world was revolutionized in the twentieth century the era of modern physics . This book, aimed at the very best students, extends the coverage of the theoretical groundwork of today's physics presented in the previous volume: