scholarly journals A particle model with extra dimensions from coadjoint Poincaré symmetry

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Andrea Barducci ◽  
Roberto Casalbuoni ◽  
Joaquim Gomis
Keyword(s):  
Lorentz Group ◽  
Extra Dimensions ◽  
Point Particle ◽  
Material Point ◽  
Particle Model ◽  
Relativistic Model ◽  
Minkowski Metric ◽  
Harmonic Motion ◽  
Poincaré Algebra ◽  
Poincaré Symmetry

AbstractStarting from the coadjoint Poincaré algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincaré algebra is able to induce a mechanism of dimensional reduction between the usual coordinates of the Minkowski space and the extra-dimensional variables which turn out to form an antisymmetric tensor under the Lorentz group. Analysing the dynamics of this model, we find that, in a particular limit, it is possible to integrate out the extra variables and determine their effect on the dynamics of the material point in the usual space time. The model describes a particle in D dimensions subject to a harmonic motion when one of the parameters of the model is negative. The result can be interpreted as a modification to the flat Minkowski metric with non trivial Riemann, Ricci tensors and scalar curvature.

scholarly journals PLANCK-SCALE RELATIVITY FROM QUANTUM κ-POINCARÉ ALGEBRA

2002 ◽  
Vol 17 (01) ◽  
pp. 1-12 ◽  
Author(s):  
J. KOWALSKI-GLIKMAN
Keyword(s):  
Planck Scale ◽  
Position Space ◽  
Commutator Algebra ◽  
Minkowski Metric ◽  
Length Contraction ◽  
Time Dilatation ◽  
Poincaré Algebra ◽  
Scale Relativity ◽  
Poincaré Symmetry ◽  
New Framework

Extending the commutator algebra of quantum κ-Poincaré symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties of positions under the action of deformed boosts. It turns out that these transformations leave invariant the quadratic form in the position space, which is the Minkowski metric and that the boosts saturate. The issues of massless and massive particles motion as well as time dilatation and length contraction in this new framework are also studied.

The kinematics of a point particle

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Internal Structure ◽  
Proper Time ◽  
World Line ◽  
Point Particle ◽  
Material Point ◽  
Spatial Extent ◽  
Geometric Representation ◽  
Mathematical Result ◽  
Point Particles ◽  
The World

This chapter discusses the kinematics of point particles undergoing any type of motion. It introduces the concept of proper time—the geometric representation of the time measured by an accelerated clock. It also describes a world line, which represents the motion of a material point or point particle P, that is, an object whose spatial extent and internal structure can be ignored. The chapter then considers the interpretation of the curvilinear abscissa, which by definition measures the length of the world line L representing the motion of the point particle P. Next, the chapter discusses a mathematical result popularized by Paul Langevin in the 1920s, the so-called ‘Langevin twins’ which revealed a paradoxical result. Finally, the transformation of velocities and accelerations is discussed.

scholarly journals Colourful Poincaré symmetry, gravity and particle actions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Joaquim Gomis ◽  
Euihun Joung ◽  
Axel Kleinschmidt ◽  
Karapet Mkrtchyan
Keyword(s):  
Field Theory ◽  
Free Particle ◽  
Three Dimensional ◽  
Background Field ◽  
Quantum Field ◽  
Symmetry Factor ◽  
Starting Point ◽  
Poincaré Algebra ◽  
Poincaré Symmetry ◽  
Three Space

Abstract We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

Monte Carlo Schemes for Radiative Transfer in Media Represented by Particle Fields

2005 ◽  
Author(s):  
Anquan Wang ◽  
Michael F. Modest
Keyword(s):  
Monte Carlo ◽  
Ray Tracing ◽  
Radiative Heat ◽  
Solid Angle ◽  
Scalar Fields ◽  
Point Particle ◽  
Particle Model ◽  
Test Problems ◽  
Combustion Modeling ◽  
Radiation Properties

Monte Carlo ray-tracing schemes are developed for the evaluation of radiative heat transfer for problems, in which the participating medium is represented by discrete point-masses, such as the flow field and scalar fields in PDF Monte Carlo methods frequently used in combustion modeling. Photon ray tracing in such cases requires that an optical thickness is assigned to each of the point-masses. Two approaches are discussed, the Point Particle Model (PPM), in which the shape of particle is not specified, and the Spherical Particle Model (SPM) in which particles are assumed to be spheres with constant radiation properties. Another issue for ray tracing in particle fields is the influence region of a ray. Two ways of modeling a ray are proposed. In the first, each ray is treated as a standard volume-less line. In the other approach, the ray is assigned a small solid angle, and is thus treated as a cone with a decaying influence function away from its center line. Based on these models, three different interaction schemes between rays and particles are proposed, i.e., Line-SPM, Cone-PPM and Cone-SPM methods, and are compared employing several test problems.

On the Predictive Capability of DNS-DEM Applied to Suspended Sediment-Turbulence Interactions

2017 ◽  
Author(s):  
Pedram Pakseresht ◽  
Sourabh V. Apte ◽  
Justin R. Finn
Keyword(s):  
Point Particle ◽  
Particle Model ◽  
Wall Region ◽  
Dynamical Interaction ◽  
Kolmogorov Length Scale ◽  
Large Particles ◽  
Wall Collision ◽  
Kolmogorov Scale ◽  
Particle Approach ◽  
Near Wall

DNS coupled with a Point-Particle based model (PP) is used to study and predict particle-turbulence interactions in an open channel flow at Reynolds number of 811 (based on the friction velocity) corresponding to the experimental observations of [Righetti & Romano, JFM 2004]. Large particles of diameter 200 microns (8.1 in wall units) with average volume loading on the order of 0.001 are simulated using four-way coupling with closure models for drag, added mass, lift, pressure, and inter-particle/particle-wall collision forces. The point-particle model is able to accurately capture the effect of particles on the fluid flow in the outer layer where particles are under resolved. However, the dynamical interaction of particle-turbulence is under predicted in the near wall region where particles size are much larger than Kolmogorov scale and grid resolution in wall-normal direction, but smaller in both stream and span wise directions. It is conjectured that due to the large size particles compared to the Kolmogorov length scale near the bed, the effect of disturbances and deflections in the flow due to presence of such large particles is not captured using Lagrangian Point-Particle approach. For this configuration, the point-particle model is not appropriate in the near wall region and a hybrid resolved particle approach may be necessary.

SUPERALGEBRAS WITH FERMIONIC GENERATORS OTHER THAN SPIN-1/2

1989 ◽  
Vol 04 (09) ◽  
pp. 831-835 ◽  
Author(s):  
CHRISTOPHER PILOT ◽  
SUBHASH RAJPOOT
Keyword(s):  
Lie Algebras ◽  
Lorentz Group ◽  
Graded Lie Algebras ◽  
Higher Spin ◽  
Poincaré Algebra

The possibility of constructing graded Lie algebras of higher spin fermionic generators is entertained. The super Poincare algebra of the generators belonging to the (1, 1/2)+(1/2, 1) representation of the Lorentz group is constructed. The closure of the algebra is demonstrated.

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