scholarly journals SCALAR FIELD THEORY ON κ-MINKOWSKI SPACE–TIME AND DOUBLY SPECIAL RELATIVITY

2005 ◽  
Vol 20 (20n21) ◽  
pp. 4925-4940 ◽  
Author(s):  
M. DASZKIEWICZ ◽  
K. IMIŁKOWSKA ◽  
J. KOWALSKI-GLIKMAN ◽  
S. NOWAK
Keyword(s):  
Scalar Field ◽  
Special Relativity ◽  
Minkowski Space ◽  
Space Time ◽  
Doubly Special Relativity ◽  
Minkowski Space Time ◽  
Point Vertex ◽  
Field Action ◽  
Poincaré Algebra ◽  
Energy And Momentum

In this paper we recall the construction of scalar field action on κ-Minkowski space–time and investigate its properties. In particular we show how the coproduct of κ-Poincaré algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space–time, equivalent to the original one. Adding the self-interaction Φ4 term we investigate the modified conservation laws. We show that the local interactions on κ-Minkowski space–time give rise to six inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.

scholarly journals Nature itself in a mirror space–time

2015 ◽  
Vol 93 (10) ◽  
pp. 1005-1008 ◽  
Author(s):  
Rasulkhozha S. Sharafiddinov
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Classical Solutions ◽  
Left Handed ◽  
Minkowski Space Time ◽  
Energy And Momentum ◽  
The Right ◽  
Structure Of Matter

The unity of the structure of matter fields with flavor symmetry laws involves that the left-handed neutrino in the field of emission can be converted into a right-handed one and vice versa. These transitions together with classical solutions of the Dirac equation testify in favor of the unidenticality of masses, energies, and momenta of neutrinos of the different components. If we recognize such a difference in masses, energies, and momenta, accepting its ideas about that the left-handed neutrino and the right-handed antineutrino refer to long-lived leptons, and the right-handed neutrino and the left-handed antineutrino are short-lived fermions, we would follow the mathematical logic of the Dirac equation in the presence of the flavor symmetrical mass, energy, and momentum matrices. From their point of view, nature itself separates Minkowski space into left and right spaces concerning a certain middle dynamical line. Thereby, it characterizes any Dirac particle both by left and by right space–time coordinates. It is not excluded therefore that whatever the main purposes each of earlier experiments about sterile neutrinos, namely, about right-handed short-lived neutrinos may serve as the source of facts confirming the existence of a mirror Minkowski space–time.

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 NON-COMMUTATIVE SPACE–TIME OF DOUBLY SPECIAL RELATIVITY THEORIES

2003 ◽  
Vol 12 (02) ◽  
pp. 299-315 ◽  
Author(s):  
J. KOWALSKI-GLIKMAN ◽  
S. NOWAK
Keyword(s):  
Phase Space ◽  
Special Relativity ◽  
Space Time ◽  
Kinematic Structure ◽  
Doubly Special Relativity ◽  
Minkowski Space Time ◽  
Space Time Structure ◽  
Commutative Space ◽  
Intrinsic Length ◽  
Heisenberg Double

Doubly Special Relativity (DSR) theory is a recently proposed theory with two observer-independent scales (of velocity and mass), which is to describe a kinematic structure underlining the theory of Quantum Gravity. We observe that there are infinitely many DSR constructions of the energy–momentum sector, each of whose can be promoted to the κ-Poincaré quantum (Hopf) algebra. Then we use the co-product of this algebra and the Heisenberg double construction of κ-deformed phase space in order to derive the non-commutative space–time structure and the description of the whole of DSR phase space. Next we show that contrary to the ambiguous structure of the energy momentum sector, the space–time of the DSR theory is unique and related to the theory with non-commutative space–time proposed long ago by Snyder. This theory provides non-commutative version of Minkowski space–time enjoying ordinary Lorentz symmetry. It turns out that when one builds a natural phase space on this space–time, its intrinsic length parameter ℓ becomes observer-independent.

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