A map which assigns each a scalar function .

Morse, P. M. and Feshbach, H. "Scalar Fields." §1.1 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 4-8, 1953.

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Weisstein, Eric W. "Scalar Field." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ScalarField.html