English

Quantum field theory without divergences

High Energy Physics - Theory 2013-05-08 v5 Mathematical Physics math.MP

Abstract

It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to {\em unmeasurable} (and hence unphysical) quantities. This is because no physical quantity can be measured in a point, but in a region, the size of which is constrained by the resolution of measuring equipment. The incorporation of the resolution into the definition of quantum fields ϕ(x)ϕ(A)(x)\phi(x)\to\phi^{(A)}(x) and appropriate change of Feynman rules results in finite values of the Green functions. The Euclidean ϕ4\phi^4-field theory is taken as an example.

Keywords

Cite

@article{arxiv.1002.2566,
  title  = {Quantum field theory without divergences},
  author = {M. V. Altaisky},
  journal= {arXiv preprint arXiv:1002.2566},
  year   = {2013}
}

Comments

6 pages, LaTeX, revtex, 2 eps figures

R2 v1 2026-06-21T14:46:29.406Z