### Abstract

By introducing the family of Feymnan maps J^{s}, we show that our earlier definition of the Feynman path integral J = J^{1} can be obtained as the analytic continuation of the Wiener integral E = J^{-i}. This leads to some new results for the Wiener and Feynman integrals. We establish a translation and Cameron-Martin formula for the Feynman maps J ^{s}, having applications to nonrelativistic quantum mechanics. We also estalish a (weak) dominated convergence theorem for J^{1} = J. © 1978 American Institute of Physics.

Original language | English |
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Pages (from-to) | 1742-1750 |

Number of pages | 9 |

Journal | Journal of Mathematical Physics |

Volume | 19 |

Issue number | 8 |

Publication status | Published - 1977 |

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## Cite this

Truman, A. (1977). The Feynman maps and the Wiener integral.

*Journal of Mathematical Physics*,*19*(8), 1742-1750.