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In page Scalar field:

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  • Vector fields, which associate a vector to every point in space. Some examples of vector fields include the air flow (wind) in meteorology.
  • Tensor fields, which associate a tensor to every point in space. For example, in general relativity gravitation is associated with the tensor field called Einstein tensor. In Kaluza–Klein theory, spacetime is extended to five dimensions and its Riemann curvature tensor can be separated out into ordinary four-dimensional gravitation plus an extra set, which is equivalent to Maxwell's equations for the electromagnetic field, plus an extra scalar field known as the "dilaton".[citation needed] (The dilaton scalar is also found among the massless bosonic fields in string theory.)