Related papers: The one example of Lorentz group
In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a…
Relativistic quantum effects on physical observables of scalar charged particles are studied. Possible peculiarities of their behavior that can be verified in an experiment can confirm several fundamental conceptions of quantum mechanics.…
We adapt the axioms of the quantum mechanics to the quantum Minkowski space-time coordinates and their transformations under the quantum Lorentz group to show how we can formulate the noncommutative special relativity and its quantum…
Lorentz gauge theory (LGT) is a feasible candidate for theory of quantum gravity in which routine field theory calculations can be carried out perturbatively without encountering too many divergences. In LGT spin of matter also gravitates.…
The Poincar\'e (inhomogeneous Lorentz) group underlies special relativity. In these lectures a consistent formalism is developed allowing an appropriate gauging of the Poincar\'e group. The physical laws are formulated in terms of points,…
A non-topological Lorentz gauge model of gravity with torsion based on Gauss-Bonnet type Lagrangian is considered. The Lagrangian differs from the Lovelock term in four-dimensional space-time and has a number of interesting features. We…
We second quantize the Fermi Lagrangian in the Lorenz gauge to obtain a covariant theory of photon quantum mechanics. Number density is real so it is interpreted as position probability density. The Hilbert space is the vector space of…
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…
It is well-known that the gravitational force can be obtained by gauging the Lorentz group, which puts gravity on the same footing as the Standard Model fields. The resulting theory - Einstein-Cartan gravity - has several crucial…
The interaction of a moving charged particle with its coherent electromagnetic field is analysed in the framework of non-relativistic quantum mechanics. It is shown that, when this interaction is taken into account, a spatially localized…
The extensive analysis of the dynamics of relativistic spinning particles is presented. Using the coadjoint orbits method the Hamiltonian dynamics is explicitly described. The main technical tool is the factorization of general Lorentz…
We perform the canonical quantization of a relativistic spinless particle moving in a curved and static spacetime. We show that the classical theory already describes at the same time both particle and antiparticle. The analyses involves…
A gauge theory of gravity based on a nonlinear realization (NLR) of the local Conform-Affine (CA) group of symmetry transformations is presented. The coframe fields and gauge connections of the theory are obtained. The tetrads and Lorentz…
The action for a $(3+1)$-dimensional particle in very special relativity is studied. It is proved that massless particles only travel in effective $(2+1)$-dimensional space-time. It is remarkable that this action can be written as an action…
In this article we consider the problem to what extent the motion of gauge-charged matter that generates the gravitational field can be arbitrary, as well as what equations are superimposed on the gauge field due to conditions of…
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…
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…
In these lectures I review the status of gravity from the point of view of the gauge principle and renormalization, the main tools in the toolbox of theoretical particle physics. In the first lecture I start from the old question "in what…
A self-consistent semi-analytical theory of beam loading in inhomogeneous accelerating structures based on the generalized theory of coupled modes is proposed. A single-mode approximation was used when the fields are represented as a sum of…
We quantize a relativistic massive complex spin-0 field and a relativistic massive spin-1/2 field on a space-time hyperboloid. We call this procedure point-form canonical quantization. Lorentz invariance of the hyperboloid implies that the…