Sep
29

Quantum field theory without divergences at a correct temporal integration

Zahid Zakir [1]

Abstract

      Quantum mechanical trajectories for particles or fields, especially in path integrals, have not temporal differentials and the path integrals are defined only on a finite slice time lattice. Therefore, in QFT all integrals on energy should be taken before turning to the limit of very small times when they are finite. The renormalizable theories are invariant under the dilatations of the time lattice slice. 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, quantum mechanics requires turning to small times only after summation over all alternatives, i.e. energy integrations in loops, and this fact leads to natural regularization of loop integrals without additional hypotheses. These justify all effective methods of regularization as various realizations of the natural temporal regularization following from the fractal nature of paths. The covariant Planck time appears as a smallest time interval due to the gravitational proper time dilation and redshift of proper frequencies near the Planck energy source. Therefore, the standard QFT with such covariant and finite regularization becomes mathematically rigorous and physically consistent.

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

Vol. 1, No 2,  p. 28 – 41, v1,   29 September 2006

Online: TPAC: 2098-003 v2,  28 September 2012; DOI: 10.9751/TPAC.2098-003


[1] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

4 Responses to “TPAC: 2098-003 v2, Vol. 1, p. 28–41”

  1. Zahid Zakir
    October 8th, 2012 at 15:49 | #1

    1. New result:
    in QFT all integrals on energy should be taken before turning to the limit of very small times when they are finite. The renormalizable theories are invariant under the dilatations of the time lattice slice.

  2. Zahid Zakir
    October 8th, 2012 at 15:51 | #2

    2. New result:
    The dilatation of the time lattice slice is a new space-time symmetry extending the Poincaré group and it has been discovered earlier in the momentum representation as the renormgroup.

  3. Zahid Zakir
    October 8th, 2012 at 15:54 | #3

    3. New result:
    Quantum mechanics requires turning to small times only after summation over all alternatives, i.e. energy integrations in loops, and this fact leads to natural regularization of loop integrals without additional hypotheses. This fact justifies all effective methods of regularization as various realizations of the natural temporal regularization following from the fractal nature of paths.

  4. Zahid Zakir
    October 8th, 2012 at 15:56 | #4

    4. New result:
    The covariant Planck time appears as a smallest time interval due to the gravitational proper time dilation and redshift of proper frequencies near the Planck energy source. As te result, the standard QFT with such covariant and finite regularization becomes mathematically rigorous and physically consistent.

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