Quantum field theory without divergences

M. V. Altaisky

Published 2010-02-12, updated 2013-05-07Version 5

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 $\phi(x)\to\phi^{(A)}(x)$ and appropriate change of Feynman rules results in finite values of the Green functions. The Euclidean $\phi^4$-field theory is taken as an example.