In terms of gauge theory on natural bundles, gauge fields are linear connections on a world manifold X, defined as Higgs field responsible for spontaneous symmetry breaking of general covariant transformations.
12.
Let us note that a true translation gauge field ( i . e ., an affine connection which yields a flat linear connection on TX ) is well defined only on a parallelizable manifold X.
13.
For instance, the Dirac operator in metric-affine gravitation theory in the presence of a general linear connection \ Gamma is well defined, and it depends just of the adapted connection \ Gamma ^ g.
14.
Given an affine connection \ Gamma on a vector bundle Y \ to X, let R and \ overline R be the curvatures of a connection \ Gamma and the associated linear connection \ overline \ Gamma, respectively.
15.
In comparison with General Relativity, dynamic variables of "'metric-affine gravitation theory "'are both a torsion where a linear connection obeys the condition that a covariant derivative of a metric equals zero.
16.
Given bundle coordinates ( 1 ) on TX, it takes the form ( 3 ) where the linear connection \ Gamma ( 4 ) and the basic soldering form \ sigma ( 6 ) are considered as independent variables.
17.
At the same time, any linear connection \ Gamma defines a principal adapted connection \ Gamma ^ g on a Lorentz reduced subbundle F ^ gX by its restriction to a Lorentz subalgebra of a Lie algebra of a general linear group GL ( 4, \ mathbb R ).
18.
Work by Hava Siegelmann and Eduardo D . Sontag has provided a proof that a specific recurrent architecture with rational valued weights ( as opposed to full precision real number-valued weights ) has the full power of a Universal Turing Machine using a finite number of neurons and standard linear connections.
19.
Conversely, every linear connection \ Gamma ( 4 ) on TX \ to X is extended to the affine one A \ Gamma on ATX which is given by the same expression ( 4 ) as \ Gamma with respect to the bundle coordinates ( 1 ) on ATX = TX, but it takes a form
20.
The impact of their work on the ley-hunting community was substantial, with one section moving in a more fully religious direction by declaring that leys could only be detected by intuition, and the other renouncing a ley line belief in favour of a more ethnographically-rooted analysis of linear connections in the landscape.
How to say linear connection in Hindi and what is the meaning of linear connection in Hindi? linear connection Hindi meaning, translation, pronunciation, synonyms and example sentences are provided by Hindlish.com.
