Finite quantum field theory with rotatory quantization and gravitational regularization

 Zahid Zakir [1]


    At quantization of harmonic rotator, a rotational mode of planar oscillator, energy spectrum is linear on frequency and equidistant, but zero-point energy in ground state can not arise. This is in agreement with generalization of uncertainty relations to non-Hermitean canonical pairs. Quantization of waves at collective rotations of a chain of harmonic rotators allows one to model the fields with charge-conjugation and gauge symmetries. In quantum field theory (QFT) at quantization of rotational modes as harmonic rotators the observables of fields are normal ordered and zero-point energy and zero-point charge of vacuum do not arise. In this case frequencies of quanta are angular speeds of rotation of field vectors in real or field spaces and two signs of helicity correspond to a particle and an antiparticle. Photons with circular polarization and complex fields are examples of such fields, spin and isospins (charges) of particles can be related by their frequencies as angular momenta and helicities of the rotating field vectors. At rotational quantization of strings there are no zero-point energy of modes and here a conformal anomaly is absent, so spacetime dimensionality and gauge group are not fixed. In QFT the fields should be averaged in small cells of space and time, where distribution and evolution of fields are described classically, and field functions on borders of cells should be sewed. Then loop integrals are finite and the renormalized theories are invariant under reduction of the size of cells (a renormgroup with the cell regularization). The Planck scale cell is smallest because of freezing of proper times in a strong external gravitational field of the loop diagram with redshifting of frequencies up to zero. In the Standard Model and quantum gravity the loop contributions of fields, with exception of scalars, are small and the perturbation theory is convergent.

PACS: 03.65.Ge, 11.30.Er, 1130.Ly, 11.90. + t, 03.65.Ge, 03.70. + k, 11.10.Gh, 11.10.Hi, 11.15.Ha, 11.10.Ly, 12.20. – m, 11.25. – w, 12.10. – g,

Keywords: quantization, charge conjugation symmetry, harmonic rotator, quantum fields, vacuum energy, renormalization, regularization, strings, anomalies

Vol. 10, No 1, p. 1 – 40, v1,     March 28, 2015
Electron.: TPAC: 5200-040 v1,    March 28, 2015 DOI: 10.9751/TPAC.5200-040

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