Scalar Field


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scalar field

[′skā·lər ′fēld]
(mathematics)
The field consisting of the scalars of a vector space.
A function on a vector space into the scalars of the vector space.
(physics)
A field which is characterized by a function of position and time whose value at each point is a scalar.

Scalar Field

 

a region with each of whose points P there is associated a number a(P) called a scalar. Mathematically, a scalar field can be defined in a given region G by specifying a scalar function a(P) of each point P of the region. Examples of scalar fields are the temperature field in a body and a density field. The methods of vector analysis are used to study scalar fields.

References in periodicals archive ?
Here the scalar field [phi], the metric 00-and 11-components [e.
So, in general terms the limit V [right arrow] [infinity] renders the system singular, and also 2[omega] + 3 [right] 0 implies [absolute value of H] [right arrow] [infinity] with the same conclusion that passing through [omega]([PSI]) = - 3/2 (corresponding to the change of the sign of the scalar field kinetic term in the Einstein frame action) would entail a space-time singularity and is impossible.
The procedures that the above four models commonly follow in the explanation of the SNeIa measurements include the following four steps: (1) Modifying the FE with an appropriate input of [LAMBDA], scalar field, perturbation, or external energy; (2) Determining the expansion rates (Hubble parameter) of the universe according to their modified FEs; (3) Submitting their expansion rates into the [D.
The material time derivative of the scalar field f (r,t) [member of] R is its substantial derivative
The scalar field that was introduced to the cosmology in various models has also been considered as a candidate of dark energy for the acceleration of the universe.
Can Brans-Dicke Scalar Field Account for Dark Energy and Dark Matter?
Van Vlaenderen obtained a scalar field for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
For instance one can begin with the inhomogeneous scalar field cosmologies with exponential potential [8], where the scalar field component of Einstein-Klein-Gordon equation can be represented in terms of:
These spaces have a single scalar field for which the field equation was written and the particular solutions were found for the spherical symmetry and for the rhombododecaedron symmetry of the space.
ij] on the boundary, needed to cancel the second derivatives in R(4) when the action is varied with the metric and scalar field, but not their normal derivatives, fixed on the boundary.
The degeneration of some parts of the flow into circles (topological features) results in in-homogeneities and gives rise to a scalar field, analogous to the gravitational field.