Abstract
We show that the two-point function of a scalar quantum field theory is a metric (i.e., a symmetric positive function satisfying the triangle inequality) on space-time (with imaginary time). It is very different from the Euclidean metric at large distances, yet agrees with it at short distances. For example, space-time has a finite diameter that is not universal. The Lipschitz equivalence class of the metric is independent of the cutoff. is not the length of the geodesic in any Riemannian metric. Nevertheless, it is possible to embed space-time in a higher dimensional space so that is the length of the geodesic in the ambient space. should be useful in constructing the continuum limit of quantum field theory with fundamental scalar particles.
- Received 5 July 2012
DOI:https://doi.org/10.1103/PhysRevD.86.065022
© 2012 American Physical Society