相关论文: Lorentz Group in Ray Optics

Many different mathematical languages have been invented to describe the ideas of Einstein's special relativity. One of the most powerful languages is the Minkowski space-time algebra of D. Hestenes. We discuss the ideas of special…

The established way of looking at special relativity is based on Einstein postulates: the principle of relativity and the constancy of the velocity of light. In the most general geometric approach to the theory of special relativity, the…

The textbook-accepted formulation of electromagnetic force was proposed by Lorentz in the 19th century, but its validity has been challenged due to incompatibility with the special relativity and momentum conservation. The Einstein-Laub…

We present a unified group-theoretical framework for superparticle theories. This explains the origin of the ``twistor-like'' variables that have been used in trading the superparticle's $\kappa$-symmetry for worldline supersymmetry. We…

One hundred years ago, in 1908, Hermann Minkowski completed his proof that Maxwell's equations are covariant under Lorentz transformations. During this process, he introduced a four-dimensional space called the Minkowskian space. In 1949,…

Category theory plays a special character in mathematics - it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this…

Owing to the existence of an invariant length at the Planck scale, Einstein special relativity breaks down at that scale. A possible solution to this problem is arguably to replace the Poincar\'e invariant Einstein special relativity by a…

The properties of the light, the Lorentz transformations and the relation mass-energy are introduced using the wave picture of the light and of the massive particles.

The definition of invariant time is fundamental to relativistic symmetry. Invariant time may be formulated as a degenerate orthogonal metric on a flat phase space with time, position, energy and momentum degrees of freedom that is also…

In a comparison of the principles of special relativity and of quantum mechanics, the former theory is marked by its relative economy and apparent explanatory simplicity. A number of theorists have thus been led to search for a small number…

In special relativity, spacetime algebra (STA) provides a powerful and insightful approach to an invariant formulation of physics. However, in this geometric algebra of spacetime, relativistic physics is usually considered a misnomer: STA…

It is shown that the group of generalized Lorentz transformations serves as relativistic symmetry group of a flat Finslerian event space. Being the generalization of Minkowski space, the Finslerian event space arises from the spontaneous…

Special relativity calculates, by means of the Lorentz gamma factor, the proper time of all inertial systems from the observer proper time, which is taken as a time standard. So, any temporal inference relies in first instance on the…

A new formal scheme is presented in which Einstein's classical theory of General Relativity appears as the common, invariant sector of a one-parameter family of different theories. This is achieved by replacing the Poincare` group of the…

When, at the end of the year 1915, both Einstein and Hilbert arrived at what were named the field equations of general relativity, both of them thought that their fundamental achievement entailed, inter alia, the realisation of a theory of…

Some studies interpret quantum measurement as being explicitly non local. Others assume the preferred frame hypothesis. Unfortunately, these two classes of studies conflict with Minkowski space-time geometry. On the contrary, in Aristotle…

Einstein's special theory of relativity starts with assumptions about how observations conducted in relatively moving inertial frames must compare. From these assumptions, conclusions can be drawn regarding the laws of physics in any one…

Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take…

An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…

A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an…