Related papers: Invariances in Physics and Group Theory
In this paper we introduce a group invariant version of the wellknown Ekeland variational principle. To achieve this, we defne the concept of convexity with respect to a group and establish a version of the theorem within this framework.…
From modern observations of gravitational interactions, it can be inferred that there is much left to discover about the fundamental gravitational field. Since the advent of the General Theory of Relativity over a century ago, we have come…
Phenomenological aspects of radiation by relativistic electrons in external field, in matter or the vicinity of matter are reviewed, among which: infrared divergence, coherence length effects, shadowing, enhancement in aligned crystals,…
The classical unified theory of Weyl is revisited. The possibility of stable extended electron model in the Einstein-Weyl space is suggested.
With the advent of high-level programming languages capable of quickly rendering three-dimensional simulations, the inclusion of computers as a learning tool in the classroom has become more prevalent. Although work has begun to study the…
Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more elegant properties with connections to the theories of Galois fields and quadratic residues.
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…
The notion that gravitation might lead to a breakdown of standard space-time structure at small distances, and that this might affect the propagation of ordinary particles has led to a program to search for violations of Lorentz invariance…
Errors pertaining to the following physical theories are discussed: the Dirac magnetic monopole theory; the Klein-Gordon equation; the Yukawa theory of nuclear force; the idea of Vector Meson Dominance; the Aharonov-Bohm effects; the idea…
There are many papers devoted to derivation of Lorentz Transformations (LT). Many people have pro posed alternative derivations. Their analysis allows looking at LT and their consequences from different standpoints. At the same time it is…
A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with…
This chapter surveys recent and less recent results on convergence of Kleinian representations, following Thurston's Double Limit and "AH(acylindrical) is compact" Theorems.
Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…
Lorentz invariance is a fundamental symmetry of both Einstein's theory of general relativity and quantum field theory. However, deviations from Lorentz invariance at energies approaching the Planck scale are predicted in many quantum…
In this paper we continue our analysis of a formulation of electrodynamics fully covariant under the full Poincar\'e group. Transformations under the four different components of the group force on us the introduction of particles, either…
The diffculties of relativistic particle theories formulated my means of canonical quantization, such as Klein-Gordon and Dirac theories, ultimately led theoretical physicists to turn on quantum field theory to model elementary particle…
[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…
An introduction to the basic ideas and methods of Chiral Perturbation Theory is presented. Several phenomenological applications of the effective Lagrangian technique to strong, electromagnetic and weak interactions are discussed.
I review the state of the art of the investigation on the structure formation in $f(R)$-gravity based on the Covariant and Gauge Invariant approach to perturbations. A critical analysis of the results, in particular the presence of…
A collection of short expository essays by the author on various topics in quantum mechanics, quantum cosmology, and physics in general.