Home > Scalar field

1 Definition

A scalar field is a function

or

The scalar field can be visualized as a n-dimensional space with a real or complex number attached to each point in the space.

The derivative of a scalar field results in a vector field called the gradient.

2 Usage

• Potential field
• In quantum field theory a scalar field is associated with spin 0 particles, like mesons. The scalar field may be real or complex valued (depending on whether it will associate a real or complex number to every point of space-time). Complex scalar fields represent charged particles.

3 Other fields

1. Vector fields, which associate a vector to every point in space. Some examples of vector fields include the electromagnetic field or the newtonian gravitational field.

1. Tensor fields, which associate a tensor to every point in space. In general relativity, gravity is associated with a tensor field. In particular, with the riemann curvature tensor. In Kaluza-Klein_theory spacetime is extended to five dimensions and its riemann curvature tensor can be separated out into ordinary four-dimensionalAbstract algebra Algebra Linear algebra Dimension (from Latin "measured out") is, in essence, the number of degrees of freedom available for movement in a space. In common usage, the dimensions of an object are the measurements that define its shape and s gravitation plus an extra set, which is equivalent to Maxwell's equationsMaxwell's equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. Introduction Maxwell's four equations express, respective for the electromagnetic fieldThe electromagnetic field EMF is composed of two related vectorial fields, the electric field and the magnetic field. This means that the vectors E and B that characterize the field each have a value defined at each point of space and time. If only E the, plus an extra scalar fieldA scalar field associates a single number (or scalar to every point in space. Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure. Definition A scalar field is a function : o known as the " dilatonIn theoretical physics, dilaton originally referred to a theoretical scalar field; as a photon refers in one sense to the electromagnetic field. For the dilaton, also known as graviscalar, it is the scalar field which appears in Kaluza-Klein theory as the".