Physical Applications of Homogeneous Balls

Introduces a unifying mathematical model to describe phenomena in different branches of physics. This book particularly develops the algebraic structure of bounded symmetric domains, highlighting the symmetry of physical laws and focusing on the interplay between algebraic structures (such as triple products) and the geometry of the domain.

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One of the mathematical challenges of modern physics lies in the development of new tools to efficiently describe different branches of physics within one mathematical framework. This text introduces precisely such a broad mathematical model, one that gives a clear geometric expression of the symmetry of physical laws and is entirely determined by that symmetry.The first three chapters discuss the occurrence of bounded symmetric domains (BSDs) or homogeneous balls and their algebraic structure in physics. The book further provides a discussion of how to obtain a triple algebraic structure associated to an arbitrary BSD; the relation between the geometry of the domain and the algebraic structure is explored as well. The last chapter contains a classification of BSDs revealing the connection between the classical and the exceptional domains.