The scalar field is called the velocity potential for the flow.

Consider a surface S on which a scalar field f is defined.

For instance, a scalar field with a positive potential can violate this condition.

For example, a scalar field cannot produce the bending of light rays.

There are a number of possible propagators for free scalar field theory.

Physically, this means that a scalar field is independent of the observer.

This is true even for a complex scalar field.

In physics, scalar fields often describe the potential energy associated with a particular force.

The dark matter can be modeled as a scalar field using two fitted parameters.

The scalar field may be real or complex valued.

His framework replaces the fine structure constant by a scalar field.

This scalar field acts together with all the rest to generate the metric.

There is a specific sense in which some scalar field theories are scale-invariant.

However, scalar fields appear in the effective field theory descriptions of many physical phenomena.

The most basic scalar field theory is the linear theory.

The scalar potential is an example of a scalar field.

In addition, we must specify a scalar field by giving a function .

However, this would be at the expense of making the connection with the quantum scalar field slightly more obscure.

In quantum field theory, a scalar field is associated with spin-0 particles.

We see that while the scalar field remains the same, the vector field now looks different.

In celestial mechanics, the 'gravitational potential' is a scalar field created by any mass, such as the earth or the Sun.

The theory contains a tensor, vector and three scalar fields.

This can also be expressed as a surface integral over the scalar field 1:

In general, the algorithm divides the scalar field first into uniform cubes.

To give an example, take two real scalar fields, φ and χ.