Related papers: Invariances in Physics and Group Theory
A possible influence of Klein's Erlangen program on physical theories is investigated. While some connections are found, it is concluded that Lie's theory of transformation groups and Lie algebras have had a much larger impact. In this…
This is an easy-reading which describes few geometric invariants which can be obtained from the group SL(2,R) within the Erlangen program of F.Klein.
Felix Klein's so-called Erlangen Program was published in 1872 as professoral dissertation. It proposed a new solution to the problem how to classify and characterize geometries on the basis of projective geometry and group theory. The…
This is an overview of Erlangen Programme at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond the traditional geometry. In this paper we demonstrate this on the example of the…
We outline a framework which generalizes Felix Klein's Erlanger Programm which he announced in 1872 after exchanging ideas with Sophus Lie.
The role of linear and projective groups of transformations in line geometry and electromagnetism is examined in accordance with Klein's Erlanger Programm for geometries. The group of collineations of real projective space is chosen as the…
The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in…
This is an outline of Erlangen Program at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond the traditional geometry. In this paper we demonstrate this on the example of the group…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
In 1917 F. Klein proposed his work on projective geometry to A. Einstein for further developments of general relativity. Klein had a peculiar way to consider the relationship between mathematics and physics, based on his Erlanger Programm…
Deformed generalized gauge groups, whch were created from physical considerations and made it possible to clarify some long-standing problems in physics, such as the problem of motion and the problem of the energy of the gravitational…
We report on recent developments towards a relativistic quantum mechanical theory of motion for a fixed, finite number of electrons, photons, and their anti-particles, as well as its possible generalizations to other particles and…
Since particle such as molecule, atom and nucleus are composite particle, it is important to recognize that physics must be invariant for both the composite particle and its constituent particles, this requirement is called particle…
In this article we show that Einstein covariance principle provides a wide opportunity in the solutions of different problems of theoretical physics. Here we apply covariance principle in some problems of classical electrodynamics and…
This paper is a contribution to Vinberg's theory of $\theta$-groups, or in other words, to Invariant Theory of periodically graded semisimple Lie algebras. One of our main tools is Springer's theory of regular elements of finite reflection…
A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the order of corrections studied explicitly. A…
The problem of the invariant classification of the orthogonal coordinate webs defined in Euclidean space is solved within the framework of Felix Klein's Erlangen Program. The results are applied to the problem of integrability of the…
We review the geometrical formulation of Quantum Mechanics to identify, according to Klein's programme, the corresponding group of transformations. For closed systems, it is the unitary group. For open quantum systems, the semigroup of…
The famous Erlangen Programme was coined by Felix Klein in 1872 as an algebraic approach allowing to incorporate fixed symmetry groups as the core ingredient for geometric analysis, seeing the chosen symmetries as intrinsic invariance of…
We survey the legacy of L.G. Kov\'acs in linear group theory, with a particular focus on classification questions.