Merches I. Scale Transitions as Foundations of Physics 2021

Textbook in PDF format

The scale transitions are essential to physical knowledge. The book describes the history of essential moments of physics, viewed as necessary consequences of the unavoidable process of scale transition, and provides the mathematical techniques for the construction of a theoretical physics founded on scale transition. The indispensable mathematical technique is analyticity, helping in the construction of space coordinate systems. The indispensable theoretical technique from physical point of view is the affine theory of surfaces. The connection between the two techniques is provided by a duality in defining the physical properties.
Foreword.
Classical Moments of Interpretation.
Recovering Some Forgotten Roots.
Theory of Regularization of Kepler Problem.
A Natural Condition of Analyticity.
The Physical Structure of Rotating Matter According to Godel.
A Geometry of Reverse Interpretation of a Fundamental Physical Structure.
Gravitation: The Case of Anisotropic Relativity.
Classical Theory of Affine Surfaces in Space.
Conclusions: Historical Line for a Theoretical Physics.
Bibliography