scholarly journals $q$ -deformed Minkowski space based on a $q$ -Lorentz algebra

1998 ◽  
Vol 5 (3) ◽  
pp. 553-566 ◽  
Author(s):  
B.L. Cerchiai ◽  
J. Wess
Keyword(s):  
Minkowski Space ◽  
Lorentz Algebra ◽  
Deformed Minkowski Space

scholarly journals DOUBLY SPECIAL RELATIVITY VERSUS κ-DEFORMATION OF RELATIVISTIC KINEMATICS

2003 ◽  
Vol 18 (01) ◽  
pp. 7-18 ◽  
Author(s):  
JERZY LUKIERSKI ◽  
ANATOL NOWICKI
Keyword(s):  
Special Relativity ◽  
Minkowski Space ◽  
Noncommutative Space ◽  
Relativistic Kinematics ◽  
Large Classes ◽  
Doubly Special Relativity ◽  
Deformed Minkowski Space ◽  
Composition Law ◽  
Poincaré Algebra ◽  
The One

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.

scholarly journals ANALYSIS ON q-DEFORMED QUANTUM SPACES

2007 ◽  
Vol 22 (01) ◽  
pp. 95-164 ◽  
Author(s):  
HARTMUT WACHTER
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Tensor Products ◽  
Main Concern ◽  
Star Products ◽  
Classical Analysis ◽  
Four Dimensions ◽  
Deformed Minkowski Space ◽  
Physical Importance ◽  
The Subject

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.

scholarly journals DIFFERENTIAL STRUCTURE ON κ-MINKOWSKI SPACE, AND κ-POINCARÉ ALGEBRA

2011 ◽  
Vol 26 (20) ◽  
pp. 3385-3402 ◽  
Author(s):  
STJEPAN MELJANAC ◽  
SAŠA KREŠIĆ-JURIĆ
Keyword(s):  
Power Series ◽  
Hopf Algebra ◽  
Minkowski Space ◽  
Differential Calculus ◽  
Weyl Algebra ◽  
Algebra Structure ◽  
Exterior Derivative ◽  
Lorentz Algebra ◽  
Poincaré Algebra ◽  
Formal Power

We construct realizations of the generators of the κ-Minkowski space and κ-Poincaré algebra as formal power series in the h-adic extension of the Weyl algebra. The Hopf algebra structure of the κ-Poincaré algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on κ-Minkowski space which is compatible with the action of the Lorentz algebra. In contrast to the conventional bicovariant calculus, the space of one-forms has the same dimension as the κ-Minkowski space.

scholarly journals LocalD=4field theory onκ-deformed Minkowski space

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

scholarly journals DIFFERENTIAL ALGEBRAS ON κ-MINKOWSKI SPACE AND ACTION OF THE LORENTZ ALGEBRA

2012 ◽  
Vol 27 (10) ◽  
pp. 1250057 ◽  
Author(s):  
STJEPAN MELJANAC ◽  
SAŠA KREŠIĆ-JURIĆ ◽  
RINA ŠTRAJN
Keyword(s):  
Power Series ◽  
Minkowski Space ◽  
Formal Power Series ◽  
Standard Approach ◽  
Lorentz Algebra ◽  
Differential Algebras ◽  
Formal Power

We propose two families of differential algebras of classical dimension on κ-Minkowski space. The algebras are constructed using realizations of the generators as formal power series in a Weyl superalgebra. We also propose a novel realization of the Lorentz algebra [Formula: see text] in terms of Grassmann-type variables. Using this realization we construct an action of [Formula: see text] on the two families of algebras. Restriction of the action to κ-Minkowski space is covariant. In contrast to the standard approach the action is not Lorentz covariant except on constant one-forms, but it does not require an extra cotangent direction.

scholarly journals A New Insight on Physical Phenomenology: A Review

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 607
Author(s):  
Stefano Bellucci ◽  
Fabio Cardone ◽  
Fabio Pistella
Keyword(s):  
Energy Density ◽  
Minkowski Space ◽  
Energy Parameter ◽  
External Electromagnetic Field ◽  
Physical Reality ◽  
Theoretical Physics ◽  
Deformed Minkowski Space ◽  
Open Questions ◽  
Parameter Values ◽  
Physical Phenomena

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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