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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.