Related papers: Weyl's search for a difference between `physical' …

Here we review a kind of post-World-War-II "Nachtrag" to H. Weyl's philosophical comments on mathematics and the natural sciences published in the middle of the 1920s. In a talk given at Z\"urich in the late 1940s, Weyl discussed…

During the ``long decade'' of transformation of mathematical physics between 1915 and 1930, H. Weyl interacted with physics in two highly productive phases and contributed to it, among others, by his widely read book on {\em Space - Time -…

H. Weyl's proposal of 1918 for generalizing Riemannian geometry by local scale gauge (later called {\em Weyl geometry}) was motivated by mathematical, philosophical and physical considerations. It was the starting point of his unified field…

We revisit Weyl's unified field theory, which arose in 1918, shortly after general relativity was discovered. As is well known, in order to extend the program of geometrization of physics started by Einstein to include the electromagnetic…

In the first attempt to introduce gauge theories in physics, Hermann Weyl, around the 1920s, proposed certain scale transformations to be a fundamental symmetry of nature. Despite the intense use of Weyl symmetry that has been made over the…

Consistency of Weyl natural gauge, Lorentz gauge and nonlinear gauge is studied in Weyl geometry. Field equations in generalized Weyl-Dirac theory show that spinless electron and photon are topological defects. Statistical metric and…

Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn by its author from physical theorizing in the early 1920s. It had a comeback in the last third of the 20th century in different contexts: scalar tensor…

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl…

During his life Weyl approached the problem of space (PoS) from various sides. Two aspects stand out as permanent features of his different approaches: the {\em unique determination of an affine connection} (i.e., without torsion in the…

Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn from physical theory in the early 1920s. It had a comeback in the last third of the 20th century in different contexts: scalar tensor theories of…

In the early phase of general relativity Elie Cartan and Hermann Weyl thought about the question of how the role of transformation groups could be transferred from classical geometry (Erlangen program) to differential geometry. They had…

One of the major developments of twentieth century physics has been the gradual recognition that a common feature of the known fundamental interactions is their gauge structure. In this talk the early history of gauge theory is reviewed,…

Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…

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…

In 1918, H. Weyl proposed a unified theory of gravity and electromagnetism based on a generalization of Riemannian geometry. In spite of its elegance and beauty, a serious objection was raised by Einstein, who argued that Weyl's theory was…

Einstein's contribution to relativity is reviewed. It is pointed out that Weyl gave first unified theory of gravitation and electromagnetism and it was different than the five dimensional theory of Kaluza. Einstein began his work on…

In 1918 Weyl introduced Weyl conformal geometry and its associated quadratic action which was the first gauge theory, of a spacetime symmetry, the Weyl gauge theory (of dilatations and Poincar\'e symmetry). The initial physical…

Weyl famously argued that if space were discrete, then Euclidean geometry could not hold even approximately. Since then, many philosophers have responded to this argument by advancing alternative accounts of discrete geometry that recover…

This paper poses some basic questions about instances (hard to find) of a special problem in 3-manifold topology. "Important though the general concepts and propositions may be with the modern industrious passion for axiomatizing and…

In the second half of the 1920s, physicists and mathematicians introduced group theoretic methods into the recently invented ``new'' quantum mechanics. Group representations turned out to be a highly useful tool in spectroscopy and in…