Theoretical Physics, Astrophysics & Cosmology

 Vol. 1, No. 2, p. 35 - 52.    29 September  2006   version 1  

Quantum Field Theory without Divergences

at a Correct Temporal Integration

Zahid Zakir

Centre for Theoretical Physics and Astrophysics

(Tashkent, Uzbekistan)

http://ctpa.theorphys.org   ctpa@theorphys.org

Abstract 

Quantum mechanical trajectories for particles or fields, particularly in path integrals, have not temporal differentials, and the path integrals can be defined only on a time lattice with a slice . But, the introduction of the time lattice is enough for the convergence of integrals on energy in loop diagrams due to the presence of highly oscillating exponents. Therefore, in QFT all integrals on energy should be calculated before the limit  while they are finite. Then, in the renormalizable theories potentially divergent terms cancel in each order of perturbation theory. Moreover, the such theories are invariant under the dilatations of the time lattice . It is a new space-time symmetry extending the Poincaré group, and it has been discovered earlier in the momentum representation as the renormgroup. Thus, the quantum mechanics requires the passing to continuous time only after the summation over all alternatives, i.e. the energy integrations in loops, and this fact leads to a natural regularization of loop divergences without additional hypotheses. As the result, all effective methods of regularization become legal ones as various realizations of the natural temporal regularization. Therefore, the such improved standard QFT at last becomes a mathematically rigorous and physically consistent theory.

PACS: 11.10.Gh, 11.10.Hi, 11.15.Ha, 11.10.Ly, 12.20.-m

Key words: quantum mechanics, path integral, quantization, renormalization,

lattice regularization, symmetries, vacuum energy, cosmological constant

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