# 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 ?
Unlike the cosmological constant, which Albert Einstein first introduced into his general theory of relativity in order for the universe to be static, the quintessence is a scalar field [PHI] that varies throughout space-time and has been modeled in various theories of gravitation such as the four-dimensional (4D) Brans-Dicke scalar-tensor gravity [3] and the five-dimensional (5D) Kaluza-Klein scalar-vector-tensor gravity (shortened by 5D gravity) [4-6].
The scalar field of 5D gravity, which has been recently related to the Higgs field of 4D particle physics in[7], were theoretically shown to be capable of polarizing the space or vacuum [8-9] and thus able to extend the optical path length of a laser beam that travels through the polarized vacuum.
This review is important because it allows identification of a scalar field contribution that was not considered in the method of derivation but influences the uniqueness of the field recovery process, and it reveals an expected and unexpected depolarizing dyad contribution.
The first objective of this section is to briefly review the uniaxial anisotropic scalar potential derivation [11] in order to identify a scalar field contribution not previously considered and to identify both an expected and unexpected depolarizing dyad contribution.
By measuring the value of alpha near a white dwarf, and comparing it with its value here and now in the laboratory, astronomers can indirectly probe whether these alpha-changing scalar fields actually exist.
Professor Barstow said that they found that any difference between the value of alpha on Earth and that measured in the strong gravitational field of the white dwarf must be smaller than a part in ten thousand, which means that any scalar fields must only weakly affect the electromagnetic force.
The early Kaluza-Klein (K-K) theory of unification was further developed with a scalar field [13], which can modify both the electromagnetic and gravitational fields.
By measuring the value of alpha near the white dwarf and comparing it with its value here and now in the laboratory we can indirectly probe whether these alpha-changing scalar fields actually exist," he said.
The solutions of the equation of motion of the scalar fields [[phi].
Also, the Reissner-Nordstrom metric [4], devised 50 years before the development of scalar fields, predicts effects which are negligible more than a few femtometers [[10.
and hence it follows at once that the scalar field specified by Eqs.

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