相关论文: Special relativity in complex vector algebra

In these notes we give an introductory unified treatment to the topics of special relativity, Lorentz transformations and the Lorentz group, Einstein velocitiy addition, and gyrogroups and gyrovector spaces. An effort has been made to…

All of the experiments supporting Einstein's Special Relativity Theory are also supportive of the Lorentz ether theory, or many other ether theories. However, a growing number of experiments show deviations from Einstein's Special…

In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting…

The target space geometry of abelian vector multiplets in ${\cal N}= 2$ theories in four and five space-time dimensions is called special geometry. It can be elegantly formulated in terms of Hessian geometry. In this review, we introduce…

I apply the algebraic framework introduced in arXiv:1101.4542v3[math.MG] to Minkowski (pseudo-Euclidean) spaces in 2, 3, and 4 dimensions. The exposition follows the template established in arXiv:1307.2917[math.MG] for Euclidean spaces. The…

This work provides a smooth and everywhere well-defined extension of Bondi-Metzner-Sachs (BMS) supertranslations into the bulk of Minkowski space. The supertranslations lead to physically distinct spacetimes, all isometric to Minkowski…

In hyperbolic space, the angle of intersection and distance classify pairs of totally geodesic hyperplanes. A similar algebraic invariant classifies pairs of hyperplanes in the Einstein universe. In dimension 3, symplectic splittings of a…

We present a way of teaching Einstein's special relativity. It starts with Galileo's relativity, the learners know from previous lectures. The lecture underlines that we can have three transformation equations for the space-time coordinates…

In the special theory of relativity, Lorentz invariance is extended in Minkowski spacetime from ideal inertial observers to actual observers by means of the hypothesis of locality, which postulates that accelerated observers are always…

We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum…

The quantum algebra of observables of the massive closed bosonic string in 1+3 dimensions has been developed so far in the rest frame of the string. In this paper a method to write this algebra in a manifestly Lorentz covariant form is…

A suitable parameterization of space-time in terms of one complex and three quaternionic imaginary units allows Lorentz transformations to be implemented as multiplication by complex-quaternionic numbers rather than matrices. Maxwell's…

Recently, [10,11], the Heisenberg Uncertainty relation and the No-Cloning property in Quantum Mechanics and Quantum Computation, respectively, have been extended to versions of Quantum Mechanics and Quantum Computation which are…

Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…

Since the special relativity can be viewed as the physics in an inverse Wick rotation of 4-d Euclid space, which is at almost equal footing with the 4-d Riemann/Lobachevski space, there should be important physics in the inverse Wick…

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard…

Special relativity was discovered at the eve of the century, but finds its roots in the 19th century efforts to understand the optics and electromagnetism of moving bodies. These roots are reviewed in Parts 1 and 2, the latter being…

We address the problem of observables in generally invariant spacetime theories such as Einstein's general relativity. Using the refined notion of an event as a ``point-coincidence'' between scalar fields that completely characterise a…

According to the basic idea of category theory, any Einstein algebra, essentially an algebraic formulation of general relativity, can be considered from the point of view of any object of the category of smooth algebras; such an object is…

The canonical formalism of the (2+2) formulation of general relativity of 4 spacetime dimensions is studied under no symmetry assumptions, where the spacetime is viewed as a local product of a 2 dimensional base manifold of Lorentzian…