This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems.
The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measure theory with potential applications in life sciences, are opened.
About the Author: Alina Gavrilut, PhD, is lecturer at the Faculty of Mathematics, Alexandru Ioan Cuza University of Iasi, Romania. Fields of competence: Mathematical Analysis - especially the Measure Theory, Nonlinear Dynamics and Quantum Physics.
Ioan Mercheş is an emeritus professor of theoretical physics at the Alexandru Ioan Cuza University of Iasi, Romania. He has co-authored 2 books published with Springer: Mechanics: An Intensive Course (2012) and Electrodynamics: An Intensive Course (2016).
Maricel Agop is professor of physics at the Gheorghe Asachi Technical University of Lasi, Romania. He was awarded the title "Doctor Honoris Causa" of the University "Vasile Alecsandri", Bacau, Romania (2013). Since 2018, he has been a correspondent member of the Academy of Romanian Scientists.
