nLab
Wiener measure

Contents

Idea

The Wiener measure is a measure on the space of continuous paths in a given manifold. The Lebesgue integral with respect to Wiener’s measure is called the Wiener integral.

The Wiener measure serves to make precise the path integral quantization for the (charged) non-relativistic particle (that of the relativistic particle may be amenable to Wiener measure methods via Wick rotation, i.e. analytic continuation to imaginary time. ).

References

A textbook account in the context of path integral quantization is