NonRiemannian metric emergent from scalar quantum field theory
Abstract
We show that the twopoint function σ(x,x^{'})=⟨[ϕ(x)ϕ(x^{'})]^{2}⟩ of a scalar quantum field theory is a metric (i.e., a symmetric positive function satisfying the triangle inequality) on spacetime (with imaginary time). It is very different from the Euclidean metric xx^{'} at large distances, yet agrees with it at short distances. For example, spacetime has a finite diameter that is not universal. The Lipschitz equivalence class of the metric is independent of the cutoff. σ(x,x^{'}) is not the length of the geodesic in any Riemannian metric. Nevertheless, it is possible to embed spacetime in a higher dimensional space so that σ(x,x^{'}) is the length of the geodesic in the ambient space. σ(x,x^{'}) should be useful in constructing the continuum limit of quantum field theory with fundamental scalar particles.
 Publication:

Physical Review D
 Pub Date:
 September 2012
 DOI:
 10.1103/PhysRevD.86.065022
 arXiv:
 arXiv:1207.0748
 Bibcode:
 2012PhRvD..86f5022K
 Keywords:

 11.10.Cd;
 11.10.Gh;
 14.80.Bn;
 84.37.+q;
 Axiomatic approach;
 Renormalization;
 Standardmodel Higgs bosons;
 Measurements in electric variables;
 High Energy Physics  Theory;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology;
 Mathematical Physics
 EPrint:
 Phys. Rev. D 86, 065022 (2012)