Mathematical Background

Part of the Progress in Mathematical Physics book series (PMP, volume 36)


The mathematical background required for the study of geometric phases in classical and quantum mechanics is rather extensive. The aim of this introductory chapter is to provide a background of some basic notions of classical differential geometry and topology. Classical differential geometry is now a well established tool in modern theoretical physics. Many classical theories like mechanics, electrodynamics, Einstein’s General Relativity or Yang-Mills gauge theories are well known examples where the geometrical methods enter in the natural and very effective way. As we shall see throughout this book, also quantum physics shows its intricate beauty when one applies an appropriate geometric framework. All this proves Wigner’s celebrated statement about the “unreasonable effectiveness” of mathematics in natural sciences.


Fibre Bundle Bianchi Identity Geometric Phasis Principal Bundle Connection Form 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  1. 1.Nicholas Copernicus UniversityTorunPoland

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