This article is about associating a scalar value with every point in a space. For the set whose members are scalars, see field.
A scalar field such as temperature or pressure, where intensity of the field is represented by different hues of colors.
In mathematics and physics, a scalar field is a function associating a single number to every point in a space – possibly physical space. The scalar may either be a pure mathematical number (dimensionless) or a scalar physical quantity (with units).
In a physical context, scalar fields are required to be independent of the choice of reference frame. That is, any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin. Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory.
and physics, a scalarfield is a function associating a single number to every point in a space – possibly physical space. The scalar may either be a...
theoretical physics, scalarfield theory can refer to a relativistically invariant classical or quantum theory of scalarfields. A scalarfield is invariant under...
scalarfield or a vector field. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function...
spin. Scalar bosons are the subset of bosons with zero-valued spin. The name scalar boson arises from quantum field theory, which demands that fields of...
traveling from one position to the other. It is a scalarfield in three-space: a directionless value (scalar) that depends only on its location. A familiar...
electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V or...
integrate over this surface a scalarfield (that is, a function of position which returns a scalar as a value), or a vector field (that is, a function which...
gravity. On a real staircase, the height above the ground is a scalar potential field: one has to go upward exactly as much as one goes downward in order...
excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson with zero spin...
scalar theories because the gravitational field is a scalar. Other proposed alternatives include scalar–tensor theories that contain a scalarfield in...
§ Generalizations below for more). A scalarfield associates a scalar value to every point in a space. The scalar is a mathematical number representing...
Look up scalar in Wiktionary, the free dictionary. Scalar may refer to: Scalar (mathematics), an element of a field, which is used to define a vector...
act on scalar and vector fields in three different ways, giving rise to three different differential operations: first, it can act on scalarfields by a...
a scalarfield or vector field that assigns, respectively, a scalar or vector to each point of space. If a tensor A is defined on a vector fields set...
Scalar theories of gravitation are field theories of gravitation in which the gravitational field is described using a scalarfield, which is required...
In quantum field theory, a quartic interaction is a type of self-interaction in a scalarfield. Other types of quartic interactions may be found under...
vector operator that operates on a vector field, producing a scalarfield giving the quantity of the vector field's source at each point. More technically...
real scalarfield. A similar process can be done for other types of fields, including the complex scalarfield, the vector field, and the Dirac field, as...
In astrophysics and cosmology scalarfield dark matter is a classical, minimally coupled, scalarfield postulated to account for the inferred dark matter...
topography Field (mathematics), type of algebraic structure Number field, specific type of the above algebraic structure Scalarfield, assignment of a scalar to...
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