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 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 κ-DEFORMED SNYDER SPACETIME

2010 ◽  
Vol 25 (08) ◽  
pp. 579-590 ◽  
Author(s):  
S. MELJANAC ◽  
D. MELJANAC ◽  
A. SAMSAROV ◽  
M. STOJIĆ
Keyword(s):  
Special Relativity ◽  
Minkowski Space ◽  
Star Product ◽  
Leibniz Rule ◽  
New Class ◽  
Special Cases ◽  
Poincaré Algebra

We present Lie-algebraic deformations of Minkowski space with undeformed Poincaré algebra. These deformations interpolate between Snyder and κ-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. Deformed Leibniz rule, the coproduct structure and star product are found. Special cases, particularly Snyder and κ-Minkowski in Maggiore-type realizations are discussed. Our construction leads to a new class of deformed special relativity theories.

scholarly journals Space-Time Defects and Group Momentum Space

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Michele Arzano ◽  
Tomasz Trześniewski
Keyword(s):  
Minkowski Space ◽  
Lorentz Group ◽  
Momentum Space ◽  
Abelian Subgroup ◽  
Space Time ◽  
Noncommutative Space ◽  
De Sitter ◽  
Maximal Abelian Subgroup ◽  
Dimensional Minkowski Space ◽  
Poincaré Algebra

We study massive and massless conical defects in Minkowski and de Sitter spaces in various space-time dimensions. The energy momentum of a defect, considered as an (extended) relativistic object, is completely characterized by the holonomy of the connection associated with its space-time metric. The possible holonomies are given by Lorentz group elements, which are rotations and null rotations for massive and massless defects, respectively. In particular, if we fix the direction of propagation of a massless defect in n+1-dimensional Minkowski space, then its space of holonomies is a maximal Abelian subgroup of the AN(n-1) group, which corresponds to the well known momentum space associated with the n-dimensional κ-Minkowski noncommutative space-time and κ-deformed Poincaré algebra. We also conjecture that massless defects in n-dimensional de Sitter space can be analogously characterized by holonomies belonging to the same subgroup. This shows how group-valued momenta related to four-dimensional deformations of relativistic symmetries can arise in the description of motion of space-time defects.

scholarly journals Doubly Special Relativity with Light-Cone Deformation

2003 ◽  
Vol 18 (24) ◽  
pp. 1711-1719 ◽  
Author(s):  
A. Błaut ◽  
M. Daszkiewicz ◽  
J. Kowalski-Glikman
Keyword(s):  
Phase Space ◽  
Special Relativity ◽  
Light Cone ◽  
Relativity Theory ◽  
Two Dimensional ◽  
Standard Quantum ◽  
Doubly Special Relativity ◽  
Poincaré Algebra ◽  
Galilean Symmetry ◽  
Special Relativity Theory

We propose a new Doubly Special Relativity theory based on the generalization of the κ-deformation of the Poincaré algebra acting along one of the null directions. We recall the quantum Hopf structure of such deformed Poincaré algebra and use it to derive the phase space commutation relations. As in the DSR based on the standard quantum κ-Poincaré algebra we find that the spacetime is noncommutative. We investigate the fate of the properties of Special Relativity in the null basis: the split of the algebra of Lorentz and momentum generators into kinematical and dynamical parts, the action of the kinematical boost M+-, and the emergence of the two-dimensional Galilean symmetry.

scholarly journals CLASSICAL VELOCITY IN κ-DEFORMED POINCARÉ ALGEBRA AND A MAXIMUM ACCELERATION

2003 ◽  
Vol 18 (07) ◽  
pp. 527-536 ◽  
Author(s):  
S. KALYANA RAMA
Keyword(s):  
Special Relativity ◽  
Particle Velocity ◽  
Simple Form ◽  
Classical Limit ◽  
Particle Trajectory ◽  
Constant Force ◽  
Maximum Acceleration ◽  
Length Scales ◽  
Doubly Special Relativity ◽  
Poincaré Algebra

We study the commutators of the κ-deformed Poincaré algebra (κPA) in an arbitrary basis. It is known that the two recently studied doubly special relativity theories correspond to different choices of κPA bases. We present another such example. We consider the classical limit of κPA and calculate particle velocity in an arbitrary basis. It has standard properties and its expression takes a simple form in terms of the variables in the Snyder basis. We then study the particle trajectory explicitly for the case of a constant force. Assuming that the spacetime continuum, velocity, acceleration, etc. can be defined only at length scales greater than x min ≠ 0, we show that the acceleration has a finite maximum.

Detection and representation of the basic peculiarities of vegetation cover by the mapping method (experience based on a research of goltsy-taiga territories)

2013 ◽  
pp. 32-47
Author(s):  
S. V. Osipov
Keyword(s):  
Vegetation Cover ◽  
Mapping Method ◽  
Vegetation Changes ◽  
Large Classes ◽  
High Rise ◽  
The Third ◽  
Altitudinal Belts ◽  
The One ◽  
Dynamic Series ◽  
River Valleys

Geobotanical mapping of the territory in riverheads Bureya of 4500 sq.km is carried out and the map of a actual vegetation cover of scale 1 : 200 000 is prepared. The legend of the map is presented in the form of the text with three-level hierarchy of classes. At the heart of structure of a legend of the map such regularities of a vegetation cover, as its latitudinal zonality / altitudinal belts, situation in a relief and dynamic series lie. The largest divisions of the legend reflect, first, change of large classes of mesocombinations of vegetation at the level of belts and, secondly, distinction in a boreal - forestry belt between a vegetation cover of tops and slopes of mountains, on the one hand, and the bottoms of river valleys, with another. Divisions of the legend of the second level reflect, first, vegetation changes in the form of high-rise and barrier changes of subbelts, secondly, distinctions of a vegetation cover in different geomorphological conditions (small and average river valleys, northern slopes, etc.). Divisions of the legend of the second level correspond to dynamic series of units of the third level. Essential addition to it are block diagrams of dynamics of a vegetation cover.

scholarly journals Minkowski box from Yangian bootstrap

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Luke Corcoran ◽  
Florian Loebbert ◽  
Julian Miczajka ◽  
Matthias Staudacher
Keyword(s):  
Minkowski Space ◽  
Wigner Function ◽  
Functional Form ◽  
A Priori ◽  
Alternative Methods ◽  
Feynman Integrals ◽  
The One

Abstract We extend the recently developed Yangian bootstrap for Feynman integrals to Minkowski space, focusing on the case of the one-loop box integral. The space of Yangian invariants is spanned by the Bloch-Wigner function and its discontinuities. Using only input from symmetries, we constrain the functional form of the box integral in all 64 kinematic regions up to twelve (out of a priori 256) undetermined constants. These need to be fixed by other means. We do this explicitly, employing two alternative methods. This results in a novel compact formula for the box integral valid in all kinematic regions of Minkowski space.

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