The Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation explores and builds upon the principles of Laurent Nottale's scale relativity. The authors address a variety of problems encountered by researchers studying the dynamics of physical systems. It explores Madelung fluid from a wave mechanics point of view, showing that confinement and asymptotic freedom are the fundamental laws of modern natural philosophy. It then probes Nottale's scale transition description, offering a sound mathematical principle based on continuous group theory. The book provides a comprehensive overview of the matter to the reader via a generalization of relativity, a theory of colors, and classical electrodynamics.

Key Features:

• Develops the concept of scale relativity interpreted according to its initial definition enticed by the birth of wave and quantum mechanics
• Provides the fundamental equations necessary for interpretation of matter, describing the ensembles of free particles according to the concepts of confinement and asymptotic freedom
• Establishes a natural connection between the Newtonian forces and the Planck's law from the point of view of space and time scale transition: both are expressions of invariance to scale transition

The work will be of great interest to graduate students, doctoral candidates, and academic researchers working in mathematics and physics.