nLab Wiener measure




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. ).


Named after Norbert Wiener‘s discussion of Brownian motion:

  • Norbert Wiener, The Average of an Analytic Functional and the Brownian Movement, Proceedings of the National Academy of Sciences of the United States of America, 7 10 (1921) 294-298 [jstor:84434]


  • Tamas Szabados, An elementary introduction to the Wiener process and stochastic integrals, Studia Scientiarum Mathematicarum Hungarica 31 (1996) 249-297 [arXiv:1008.1510]


See also:

A textbook account in the context of path integral quantization:

  • Barry Simon, around p. 49 in: Functional integration and quantum physics, AMS Chelsea Publ., Providence, 2005

Last revised on November 30, 2023 at 09:36:33. See the history of this page for a list of all contributions to it.