An Algebraic Geometric Approach to Separation of Variables [Paperback]

Konrad Sch?bel aims to lay the foundations for a consequent algebraic geometric treatment of variable Separation, which?is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads.

I am particularly impressed by his mastery of a variety of techniques and his ability to show clearly how they interact to produce his results.? ?(Jim Stasheff)

The Foundation: The Algebraic Integrability Conditions.- The Proof of Concept: A Complete Solution for the 3-Sphere.- The Generalisation: A Solution for Spheres of Arbitrary Dimension.- The Perspectives: Applications and Generalisations.

Konrad Sch?bel studied physics and mathematics at Friedrich-Schiller University Jena (Germany) and Universidad de Granada (Spain) and obtained his PhD at the Universit? de Provence Aix-Marseille I (France). He now holds a postdoc position at Friedrich-Schiller University Jena and works as a research and development engineer for applications in clinical ultrasound diagnostics.

Konrad Sch?bel aims to lay the foundations for a consequent algebraic geometric treatment of variable separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modlC%