# 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 ?
Then, by using the conclusion in Equation (29), the discrete scalar wave equation with a boundary term can be written as:
Here, [bar.K] is an [N.sub.1] x [N.sub.1] matrix with only [N.sub.1,[partial derivative]] nonzero rows, similar with [[partial derivative].sub.n][bar.g] introduced for scalar wave. The (i,j) element [[[bar.K]].sub.i,j] associated with j-th primal edge and i-th dual face at surface, which only has one edge [L.sup.[partial derivative].sub.i] on the surface, is defined as:
Mann, "Scalar wave falloff in asymptotically anti-de Sitter backgrounds," Physical Review D, vol.
Mann, "Scalar wave falloff in topological black hole backgrounds," Physical Review D, vol.
This description above of in-and out-waves is almost identical to the quantum waves of the electron that can be obtained rigorously using a scalar wave equation in Section H.
Wolff, (6,7) Mead, (8) and Haselhurst (13) explored the Scalar Wave Equation and found that its solutions form a quantum-wave structure, possessing all the electron's experimental properties, eliminating the paradoxes of quantum mechanics and cosmology.
Quantum waves exist in space and are solutions of a scalar wave equation

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