Special Relativity in Minkowski Space

2019 ◽  
pp. 239-266
Author(s):  
Antonio Romano ◽  
Mario Mango Furnari
Keyword(s):  
Special Relativity ◽  
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 Investigation of a curve using Frenet frame in the lightlike cone

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 175-181
Author(s):  
Mihriban Kulahci
Keyword(s):  
Special Relativity ◽  
Minkowski Space ◽  
Frenet Frame ◽  
Mathematical Methods ◽  
3 Dimensional ◽  
Mathematics And Physics

AbstractOften times the language of mathematics is used to formulate physical theories. For example, as in this paper, while Minkowski space or the theory of special relativity were studying, their formulation was given by means of mathematical methods. In this manuscript, we study spacelike normal curves lying entirely in the 2-dimensional and 3-dimensional lightlike cone. In particular, some related theorems and definitions are also given. The study of representations of spacelike normal curves in the lightlike cone has led to the existence of different areas of mathematics and physics.

scholarly journals How Does Spacetime “Tell an Electron How to Move”?

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2283
Author(s):  
Garnet Ord
Keyword(s):  
Special Relativity ◽  
Minkowski Space ◽  
Continuum Limit ◽  
Minkowski Spacetime ◽  
Discrete Space ◽  
Kinematics And Dynamics ◽  
Uniform Motion ◽  
Classical Particles

Minkowski spacetime provides a background framework for the kinematics and dynamics of classical particles. How the framework implements the motion of matter is not specified within special relativity. In this paper we specify how Minkowski space can implement motion in such a way that ’quantum’ propagation occurs on appropriate scales. This is done by starting in a discrete space and explicitly taking a continuum limit. The argument is direct and illuminates the special tension between ’rest’ and ’uniform motion’ found in Minkowski space, showing how the formal analytic continuations involved in Minkowski space and quantum propagation arise from the same source.

scholarly journals I: Geometric Interpretation of the Minkowski Metric

2019 ◽  
Author(s):  
Thomas Merz
Keyword(s):  
Euclidean Space ◽  
Special Relativity ◽  
Minkowski Space ◽  
Lie Algebras ◽  
Geometric Interpretation ◽  
Minkowski Metric ◽  
Basis Element ◽  
Direct Mapping

A geometric interpretation of the Minkowski metric and thus of phenomena in special relativity is provided. It is shown that a change of basis in Minkowski space is the equivalent of a change of basis in Euclidean space if one basis element is replaced by its dual element. The methodology of the proof includes infinitesimal changes of basis using the Lie-algebras of the involved groups. As a consequence, a direct mapping between Euclidean and Minkowski space is defined.

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.

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