scholarly journals Representation of 3D and 4D Objects Based on an Associated Curved Space and a General Coordinate Transformation Invariant Description

2006 ◽  
Vol 2007 (1) ◽  
Author(s):  
Eric Paquet
Keyword(s):  
Coordinate Transformation ◽  
Curved Space ◽  
Invariant Description ◽  
General Coordinate Transformation

Study of Large Scale Measurement Method Based on Leapfrog Principle

2011 ◽  
Vol 130-134 ◽  
pp. 1560-1563
Author(s):  
Long Jiang Zheng ◽  
Xue Li ◽  
Ling Ling Qin ◽  
Hong Bin Chen ◽  
Xue Gao ◽  
...  
Keyword(s):  
Coordinate Transformation ◽  
Large Scale ◽  
Manufacturing Industry ◽  
Coordinate Measuring Machine ◽  
Measuring Method ◽  
Measuring System ◽  
Wide Range ◽  
General Coordinate Transformation ◽  
Measuring Machine ◽  
The Mathematical Model

At present，large scale and space coordinates measuring system with wide-range and high-precision has been widely used in modern manufacturing industry. In this paper, large scale measuring method based on leapfrog principle of flexible three coordinate measuring machine is described. The mathematical model of coordinate transformation is built and the general coordinate transformation formula after number of times leapfrogging is derived. The best positioning and each step of leapfrog are given.

scholarly journals AN INVARIANT APPROACH TO DYNAMICAL FUZZY SPACES WITH A THREE-INDEX VARIABLE

2006 ◽  
Vol 21 (13) ◽  
pp. 1017-1028 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Linear Transformation ◽  
Coordinate Transformation ◽  
General Linear ◽  
Variable Formula ◽  
Fuzzy Space ◽  
General Coordinate Transformation ◽  
Invariant Approach ◽  
Invariant Tensors

A dynamical fuzzy space might be described by a three-index variable [Formula: see text], which determines the algebraic relations [Formula: see text] among the functions fa on the fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on fa. We study equations for the three-index variable invariant under the general linear transformation and show that the solutions can be generally constructed from the invariant tensors of Lie groups. As specific examples, we study SO(3) symmetric solutions and discuss the construction of a scalar field theory on a fuzzy two-sphere within this framework.

scholarly journals GRAVITY FROM DIRAC EIGENVALUES

1998 ◽  
Vol 13 (06) ◽  
pp. 479-494 ◽  
Author(s):  
GIOVANNI LANDI ◽  
CARLO ROVELLI
Keyword(s):  
General Relativity ◽  
Jacobian Matrix ◽  
Equations Of Motion ◽  
Scaling Law ◽  
Einstein Equations ◽  
Fermion Field ◽  
Spectral Action ◽  
Curved Space ◽  
Invariant Description ◽  
Infinite Set

We study a formulation of Euclidean general relativity in which the dynamical variables are given by a sequence of real numbers λn, representing the eigenvalues of the Dirac operator on the curved space–time. These quantities are diffeomorphism-invariant functions of the metric and they form an infinite set of "physical observables" for general relativity. Recent work of Connes and Chamseddine suggests that they can be taken as natural variables for an invariant description of the dynamics of gravity. We compute the Poisson brackets of the λn's, and find that these can be expressed in terms of the propagator of the linearized Einstein equations and the energy-momentum of the eigenspinors. We show that the eigenspinors' energy-momentum is the Jacobian matrix of the change of coordinates from the metric to the λn's. We study a variant of the Connes–Chamseddine spectral action which eliminates a disturbing large cosmological term. We analyze the corresponding equations of motion and find that these are solved if the energy momenta of the eigenspinors scale linearly with the mass. Surprisingly, this scaling law codes Einstein's equations. Finally we study the coupling to a physical fermion field.

THE GAUGE-INVARIANT THEORY OF HIGHER SPIN FIELDS IN CURVED SPACE

1991 ◽  
Vol 06 (10) ◽  
pp. 1693-1700 ◽  
Author(s):  
I.G. AVRAMIDI
Keyword(s):  
Invariant Theory ◽  
Gauge Invariant ◽  
Curved Space ◽  
Invariant Action ◽  
Invariant Description ◽  
Higher Spin ◽  
Spin Fields ◽  
Higher Spin Fields

It is shown that the gauge-invariant description of higher spin fields requires a nonlocal generalisation of the theory. Nonlocal gauge-invariant action functionals for spin 3/2 field and tensor spin 2 field in curved space are constructed.

Sign in / Sign up

Export Citation Format

Share Document