Related papers: Geometry and physics of today
In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics,…
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings,…
The kinematical part of general theory of deformational structures on smooth manifolds is developed. We introduce general concept of d-objects deformation, then within the set of all such deformations we develop some special algebra and…
A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…
The gauge symmetry is one of the most important concepts in modern physics, but there are two conflicting views on its meaning or interpretation. The standard view is that local gauge symmetry is the basis of the pursue of fundamental…
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…
In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential…
We develop some foundations for the theory of formal derived algebraic geometry, which parallel the theory of formal spectral algebraic geometry by Jacob Lurie. For this, we establish a close connection between algebro-geometric objects in…
Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak…
An action of a Lie algebra $\frak g$ on a manifold $M$ is just a Lie algebra homomorphism $\zeta:\frak g\to \frak X(M)$. We define orbits for such an action. In general the space of orbits $M/\frak g$ is not a manifold and even has a bad…
The geometries of spaces having as groups the real orthogonal groups and some of their contractions are described from a common point of view. Their central extensions and Casimirs are explicitly given. An approach to the trigonometry of…
This lecture note is hopefully helpful to undergraduate and postgraduate students or beginning Ph.D students both in theoretical physics and in applied mathematics. Modern terminology in differential geometry has been discussed in the book…
Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics…
The geometric properties of General Relativity are reconsidered as a particular nonlinear interaction of fields on a flat background where the perceived geometry and coordinates are "physical" entities that are interpolated by a patchwork…
This is the Preface to the special issue of 'International Journal of Geometric Methods in Modern Physics', v.3, N.1 (2006) dedicated to the 50th aniversary of gauge gravitation theory. It addresses the geometry underlying gauge gravitation…
Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space…
The field equation of orthodox general relativity are written in the context of a geometry with non-vanishing torsion, the Absolute Parallelism (AP) geometry. An AP-structure, with homogeneity and isotropy, is used for cosmological…
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector…
This note focuses the problem of motivating the use of gauge symmetries (being the identity on the observables) from general principles, beyond their practical success, starting from global gauge symmetries and then by emphasizing the…