relativity, a scalar field solution is an exact solution of the Einstein field equation in which the gravitational field is due entirely to the field energy...

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...

theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under...

In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though...

traveling from one position to the other. It is a scalar field in three-space: a directionless value (scalar) that depends only on its location. A familiar...

written as the theory of a scalar field, Φ, which is the gravitational potential in joules per kilogram of the gravitational field g = −∇Φ, see Gauss's law...

similar to that of the Dirac equation. The equation solutions include a scalar or pseudoscalar field[clarification needed]. In the realm of particle physics...

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...

In physics, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. A weather map...

integrate over this surface a scalar field (that is, a function of position which returns a scalar as a value), or a vector field (that is, a function which...

("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector...

fields, which include scalar and vector fields as special cases. For example, if there are m {\displaystyle m} real-valued scalar fields, φ 1 , … , φ m {\displaystyle...

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...

on the following ingredients: A unit vector field; A dynamical scalar field; A nondynamical scalar field; A matter Lagrangian constructed using an alternate...

scalar theories because the gravitational field is a scalar. Other proposed alternatives include scalar–tensor theories that contain a scalar field in...

slope field (also called a direction field) is a graphical representation of the solutions to a first-order differential equation of a scalar function...

of a scalar–tensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of general...

In theoretical physics, scalar electrodynamics is a theory of a U(1) gauge field coupled to a charged spin 0 scalar field that takes the place of the...

In quantum field theory, a quartic interaction is a type of self-interaction in a scalar field. Other types of quartic interactions may be found under...

} Given vector fields V, W defined on S and a smooth function f defined on S, the operations of scalar multiplication and vector addition...

{Q}{r^{2}}}{\hat {\mathbf {r} }}\,.} The electric field is conservative, and hence is given by the gradient of a scalar potential, V(r) E ( r ) = − ∇ V ( r ) ....

In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To...

quantum field theory, an auxiliary field is one whose equations of motion admit a single solution. Therefore, the Lagrangian describing such a field A {\displaystyle...

different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product. The scalar triple product (also called...

a scalar field is a scalar field, and the Fourier transform of a vector field is a vector field of same dimension. Now consider the following scalar and...

In physics, a unified field theory (UFT) is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles...

(quantum field theory) Scalar field dark matter Scalar field solution Scalar field theory Scalar meson Scalar multiplication Scalar potential Scalar theories...

In the case of the real scalar field, the existence of these operators was a consequence of the decomposition of solutions of the classical equations...

surfaces, piecemeal solutions can be stitched together to provide a description of the magnetic field at all points in space. The scalar potential is a useful...

An electromagnetic field (also EM field) is a physical field, mathematical functions of position and time, representing the influences on and due to electric...