2003 ◽  
Vol 18 (01) ◽  
pp. 7-18 ◽  
Author(s):  
JERZY LUKIERSKI ◽  
ANATOL NOWICKI

We argue that the so-called doubly special relativity (DSR), recently proposed by Amelino-Camelia et al.1,2 with deformed boost transformations identical with the formulae for κ-deformed kinematics in bicrossproduct basis is classical special relativity in nonlinear disguise. The choice of symmetric composition law for deformed four-momenta as advocated in Refs. 1 and 2 implies that DSR is obtained by considering the nonlinear four-momenta basis of classical Poincaré algebra and it does not lead to noncommutative space–time. We also show how to construct two large classes of doubly special relativity theories — generalizing the choice in Refs. 1 and 2 and the one presented by Magueijo and Smolin.3 The older version of deformed relativistic kinematics, differing essentially from classical theory in the coalgebra sector and leading to noncommutative κ-deformed Minkowski space is provided by quantum κ-deformation of Poincaré symmetries.


2007 ◽  
Vol 22 (01) ◽  
pp. 95-164 ◽  
Author(s):  
HARTMUT WACHTER

A q-deformed version of classical analysis is given to quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. The subject is presented in a rather complete and self-contained way. All relevant notions are introduced and explained in detail. The different possibilities to realize the objects of q-deformed analysis are discussed and their elementary properties are studied. In this manner attention is focused on star products, q-deformed tensor products, q-deformed translations, q-deformed partial derivatives, dual pairings, q-deformed exponentials, and q-deformed integration. The main concern of this work is to show that these objects fit together in a consistent framework, which is suitable to formulate physical theories on quantum spaces.


1974 ◽  
Vol 52 (1) ◽  
pp. 40-48 ◽  
Author(s):  
Antoine Yaccarini

A comparison is made, between three methods for visualizing the Minkowski space, in view of their application to relativistic kinematics.The velocity manifold method, in which a vector is represented by a point on the upper sheet of the unit-radius hyperboloid, presents two advantages: there is no distortion of angles, and the method is independent of the choice of any particular frame or observer. It is, however, limited to the representation of positive timelike vectors.The Cayley map method allows the representation of spacelike as well as timelike vectors, but it has two drawbacks: it distorts the angles, and it depends on the choice of a reference system.In the third method, the use of a unified space–time formalism permits one to visualize any kind of vector. This method generalizes the velocity manifold method, and presents the same two advantages: it provides us with a conformal representation, which is independent of any particular observer.We also present a rather concise comparison between two covariant methods of calculation, considered from the point of view of relativistic kinematics. One method is the familiar tensor calculus; the other is the spinor calculus, based on the representation of four-vectors by matrices.


2000 ◽  
Vol 62 (2) ◽  
Author(s):  
P. Kosiński ◽  
J. Lukierski ◽  
P. Maślanka

1968 ◽  
Vol 8 (2) ◽  
pp. 134-160 ◽  
Author(s):  
G. Szekeres

The aim of this paper is, briefly, an axiomatization of relativistic kinematics. Before stating the aims in more precise terms, a few words about the origins of the paper will be necessary. The idea of a revision of the axiomatic foundations of relativistic kinematics came up in discussions with the late M. L. Urquhart at the 1963 (3rd) Summer Research Institute of the Australian Mathematical Society, and it was a suggestion by Urquhart which started off the present investigation. Following his suggestion I prepared a preliminary draft containing the outlines of an axiomatic system for Minkowski space-time and passed it on to him. Shortly before his death Urquhart asked Professor D. Elliott to send the manuscript back to me and it was this manuscript which formed the nucleus of the present paper.


Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 607
Author(s):  
Stefano Bellucci ◽  
Fabio Cardone ◽  
Fabio Pistella

After a brief digression on the current landscape of theoretical physics and on some open questions pertaining to coherence with experimental results, still to be settled, it is shown that the properties of the deformed Minkowski space lead to a plurality of potential physical phenomena that should occur, provided that the resulting formalisms can be considered as useful models for the description of some aspects of physical reality. A list is given of available experimental evidence not easy to be interpreted, at present, by means of the more established models, such as the standard model with its variants aimed at overcoming its descriptive limits; this evidence could be useful to verify the predictions stemming from the properties of the deformed Minkowski space. The list includes anomalies in the double-slit-like experiments, nuclear metamorphosis, torsional antennas, as well as the physical effect of the “geometric vacuum” (as defined in analogy with quantum vacuum), in the absence of external electromagnetic field, when crossing critical thresholds of energy parameter values, energy density in space and energy density in time. Concrete opportunities are suggested for an experimental exploration of phenomena, either already performed but still lacking a widely accepted explanation, or conceivable in the application of the approach here presented, but not tackled until now. A tentative list is given with reference to experimental infrastructures already in operation, the performances of which can be expanded with limited additional resources.


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