scholarly journals Modified Lorentz transformations in deformed special relativity

2017 ◽  
Vol 32 (15) ◽  
pp. 1750086
Author(s):  
G. Salesi ◽  
M. Greselin ◽  
L. Deleidi ◽  
R. A. Peruzza
Keyword(s):  
Special Relativity ◽  
Particle Physics ◽  
Natural Extension ◽  
Planck Scale ◽  
Lorentz Factor ◽  
Lorentz Transformations ◽  
Elementary Particle Physics ◽  
Recent Approach ◽  
Energy And Momentum ◽  
Energy Relations

We have extended a recent approach to Deformed Special Relativity based on deformed dispersion laws, entailing modified Lorentz transformations and, at the same time, noncommutative geometry and intrinsically discrete space–time. In so doing we have obtained the explicit form of the modified Lorentz transformations for a special class of modified momentum-energy relations often found in literature and arising from quantum gravity and elementary particle physics. Actually, our theory looks as a very simple and natural extension of special relativity to include a momentum cutoff at the Planck scale. In particular, the new Lorentz transformations do imply that for high boost speed [Formula: see text] the deformed Lorentz factor does not diverge as in ordinary relativity, but results to be upper bounded by a large finite value of the order of the ratio between the Planck mass and the particle mass. We have also predicted that a generic boost leaves unchanged Planck energy and momentum, which result invariant with respect to any reference frame. Finally, through matrix deformation functions, we have extended our theory to more general cases with dispersion laws containing momentum-energy mixed terms.

scholarly journals KINEMATICAL SOLUTION OF THE UHE-COSMIC-RAY PUZZLE WITHOUT A PREFERRED CLASS OF INERTIAL OBSERVERS

2003 ◽  
Vol 12 (07) ◽  
pp. 1211-1226 ◽  
Author(s):  
GIOVANNI AMELINO-CAMELIA
Keyword(s):  
Special Relativity ◽  
Particle Physics ◽  
Planck Scale ◽  
Cosmic Ray ◽  
Lorentz Symmetry ◽  
Relativity Theory ◽  
Lorentz Transformations ◽  
Doubly Special Relativity ◽  
Energy Scenario ◽  
Special Relativity Theory

Among the possible explanations for the puzzling observations of cosmic rays above the GZK cutoff there is growing interest in the ones that represent kinematical solutions, based either on general formulations of particle physics with small violations of Lorentz symmetry or on a quantum-gravity-motivated scheme for the breakdown of Lorentz symmetry. An unappealing aspect of these cosmic-ray-puzzle solutions is that they require the existence of a preferred class of inertial observers. Here I propose a new kinematical solution of the cosmic-ray puzzle, which does not require the existence of a preferred class of inertial observers. My proposal is a new example of a type of relativistic theories, the so-called "doubly-special-relativity" theories, which have already been studied extensively over the last two years. The core ingredient of the proposal is a deformation of Lorentz transformations in which also the Planck scale Ep (in addition to the speed-of-light scale c) is described as an invariant. Just like the introduction of the invariant c requires a deformation of the Galileian transformations into the Lorentz transformations, the introduction of the invariant Ep requires a deformation of the Lorentz transformations, but there is no special class of inertial observers. The Pierre Auger Observatory and the GLAST space telescope should play a key role in future developments of these investigations. I also emphasize that the doubly-special-relativity theory here proposed, besides providing a solution for the cosmic-ray puzzle, is also the first doubly-special-relativity theory with a natural description of macroscopic bodies, and may find applications in the context of a recently-proposed dark-energy scenario.

scholarly journals New measurement method corrected a failure in special relativity

2021 ◽  
Author(s):  
Viktor Schatz
Keyword(s):  
Special Relativity ◽  
Lorentz Factor ◽  
Alternative Interpretation ◽  
Lorentz Transformations ◽  
Measuring Process ◽  
Measuring Devices ◽  
Reasoning Problem ◽  
New Interpretation ◽  
High Level ◽  
Spatial Locations

Abstract A logical reasoning problem in the Special Relativity interpretation of the Lorentz transformation was discovered and corrected by introducing an alternative interpretation of Lorentz transformations with a relativistic measuring process based on both, stretched time and length units, whereby the measurements as a consequence measure a shortened distance and time lines as variables due to used units. The space shuttles are getting longer instead of shorter and a barn-pole paradox does not occur. The spatial locations remain in their locations and space is not contracted and not changed. The failure is that by contracting both units and distance the Lorentz factor is eliminated and relativity was vanished. The elementary particles have their own measuring devices for time and length in the form of wavelengths and frequencies and they read distances and durations of different lengths from space using their own relativistically different units. The new interpretation is covered by the two postulates of Einstein. This is a sensational result too in view of all dramatic and romantic history as there is really a failure discovered. The Lorentz transformations remain being in use with another method. The new theory and the discovered problems of logical failures are explained vividly in the same manner as Special Relativity was using easy be thought samples. Reader do not need a high level of mathematics to be fit for as it is a more qualitatively thematic for every one who is interested in relativity matters.

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

Gauge Field Theory in Natural Geometric Language

2020 ◽  
Author(s):  
Daniel Canarutto
Keyword(s):  
Particle Physics ◽  
Quantum Physics ◽  
Brst Symmetry ◽  
Natural Extension ◽  
Integrated Approach ◽  
Arbitrary Spin ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Standard View ◽  
Spinor Bundle

This monograph addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a not-too-short, integrated approach that exploits standard and non-standard notions in natural geometric language. The role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. Two-spinors yield a partly original ‘minimal geometric data’ approach to Einstein-Cartan-Maxwell-Dirac fields. The gravitational field is jointly represented by a spinor connection and by a soldering form (a ‘tetrad’) valued in a vector bundle naturally constructed from the assumed 2-spinor bundle. We give a presentation of electroweak theory that dispenses with group-related notions, and we introduce a non-standard, natural extension of it. Also within the 2-spinor approach we present: a non-standard view of gauge freedom; a first-order Lagrangian theory of fields with arbitrary spin; an original treatment of Lie derivatives of spinors and spinor connections. Furthermore we introduce an original formulation of Lagrangian field theories based on covariant differentials, which works in the classical and quantum field theories alike and simplifies calculations. We offer a precise mathematical approach to quantum bundles and quantum fields, including ghosts, BRST symmetry and anti-fields, treating the geometry of quantum bundles and their jet prolongations in terms Frölicher's notion of smoothness. We propose an approach to quantum particle physics based on the notion of detector, and illustrate the basic scattering computations in that context.

scholarly journals Dynamical Symmetries of the H Atom, One of the Most Important Tools of Modern Physics: SO(4) to SO(4,2), Background, Theory, and Use in Calculating Radiative Shifts

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1323 ◽  
Author(s):  
G. Jordan Maclay
Keyword(s):  
Hydrogen Atom ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Bound States ◽  
Integrated Treatment ◽  
Invariance Group ◽  
Elementary Particle Physics ◽  
Background Theory ◽  
Modern Physics ◽  
History Of

Understanding the hydrogen atom has been at the heart of modern physics. Exploring the symmetry of the most fundamental two body system has led to advances in atomic physics, quantum mechanics, quantum electrodynamics, and elementary particle physics. In this pedagogic review, we present an integrated treatment of the symmetries of the Schrodinger hydrogen atom, including the classical atom, the SO(4) degeneracy group, the non-invariance group or spectrum generating group SO(4,1), and the expanded group SO(4,2). After giving a brief history of these discoveries, most of which took place from 1935–1975, we focus on the physics of the hydrogen atom, providing a background discussion of the symmetries, providing explicit expressions for all of the manifestly Hermitian generators in terms of position and momenta operators in a Cartesian space, explaining the action of the generators on the basis states, and giving a unified treatment of the bound and continuum states in terms of eigenfunctions that have the same quantum numbers as the ordinary bound states. We present some new results from SO(4,2) group theory that are useful in a practical application, the computation of the first order Lamb shift in the hydrogen atom. By using SO(4,2) methods, we are able to obtain a generating function for the radiative shift for all levels. Students, non-experts, and the new generation of scientists may find the clearer, integrated presentation of the symmetries of the hydrogen atom helpful and illuminating. Experts will find new perspectives, even some surprises.

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