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Path Integral

Let gamma be a path given parametrically by sigma(t). Let s denote arc length from the initial point. Then

int_gammaf(s)ds=int_a^bf(sigma(t))|sigma^'(t)|dt
(1)
=int_a^bf(x(t),y(t),z(t))|sigma^'(t)|dt,
(2)

where gamma:{sigma(t):a<=t<=b}.

See also

Contour Integral, Integral, Line Integral, Path

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References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Evaluation of Functions by Path Integration." §5.14 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 201-204, 1992.

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Path Integral

Cite this as:

Weisstein, Eric W. "Path Integral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PathIntegral.html

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