A new perspective on functional integration

  title={A new perspective on functional integration},
  author={Pierre Cartier and Cecile DeWitt-Morette},
  journal={Journal of Mathematical Physics},
The core of this article is a general theorem with a large number of specializations. Given a manifold N and a finite number of one‐parameter groups of point transformations on N with generators Y,X(1),...,X(d), we obtain, via functional integration over spaces of pointed paths on N (paths with one fixed point), a one‐parameter group of functional operators acting on tensor or spinor fields on N. The generator of this group is a quadratic form in the Lie derivatives LX(α) in the X(α)‐direction… 

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