Related papers: Luis Santal\'o and classical field theory
During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge theory of the Weyl-Cartan-Yang-Mills type. The present text offers commentaries on the articles from the most prominent…
Albert Einstein visited Spain only once, precisely one hundred years ago. The circumstances, of a very different kind, of this visit will be explained here. In special, some important events happened to Einstein during that period, which,…
We show the relevance of the logarithmic integral function in the development of mathematics in the first half of the 19th century. Its importance involved first level mathematicians such as Euler, Gauss, Bessel, Riemann. Our perspective is…
A conservative extension of general relativity by integrable Weyl geometry is formulated, and a new class of cosmological models ({\em Weyl universes}) is introduced and studied. A short discussion of how these new models behave in the…
We comment on the paper [1] by Albert Einstein from 1918 to Willem De Sitter's solution [2] of the Einstein field equation from today's point of view. To this end, we start by describing the geometry of the De Sitter space-time and present…
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics…
In this article, we review the current status of Finsler-Lagrange geometry and generalizations. The goal is to aid non-experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to…
The aim of this paper (Part III) is formulating GR as a scalar field theory. The basic structural elements of it are a generating function, a generalized density and a generalized temperature. One of the axioms of this theory is a…
Einstein is usually revered as the father of special and general relativity. In this article I demonstrate that he is also the father of Solid State Physics, or even his broader version known as Condensed Matter Physics (including liquids).…
This year marks the 100th anniversary of Einstein's General Theory of Relativity (1915-2015). The first nontrivial solution of the Einstein field equations was derived by Karl Schwarzschild in 1916. This Note will focus mainly on the…
Einstein's general relativity is increasingly important in contemporary physics on the frontiers of both the very largest distance scales (astrophysics and cosmology) and the very smallest(elementary particle physics). This paper makes the…
Giulio Racah's name is known world wide in physics due to the mathematical methods he developed that are based on tensor operators and continuous groups. These methods revolutionized spectroscopy, and they are currently essential research…
Isaak Moiseevich Yaglom deduced complete classification of geometric spaces. In this work, supposed to your attention, author formalizes Yaglom's approach and constructs uniform theory of geometric spaces on analytic level. Among its…
A scalar theory of gravity extending Newtonian gravity to include field energy as its source is developed. The physical implications of the theory are probed through its spherically symmetric (source) solutions. The aim is to demonstrate…
From modern observations of gravitational interactions, it can be inferred that there is much left to discover about the fundamental gravitational field. Since the advent of the General Theory of Relativity over a century ago, we have come…
The aim of this work is to use the notions of Riemann's geometry introduced in Part I, to analyze the foundations of Einstein's theory of general relativity.
Since the mid-1920s, different strands of research used stars as "physics laboratories" for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is…
This work is an introduction to modern mathematical physics. We begin with Maxwell laws and vector calculus, pass next to consider the action and the Feynman integral in quantum mechanics, next relativity and differential geometry to…
This essay discusses the development of key geometric ideas in the 19th century which led to the formulation of the concept of an abstract manifold (which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl in 1913. This…
The unification of all physical fields into one mathematical object and the derivation of all physical field equations from that object in one framework is a long-lasting endeavor in fundamental physics. We suggest a new approach to achieve…