Krein regularization of quantum chromodynamics

In this paper, we use Krein regularization to study certain standard computations in quantum chromodynamics (QCD). In this method, the auxiliary modes[Formula: see text]— those with negative norms[Formula: see text]— are employed to calculate the quark self-energy, vacuum polarizations and vertex functions. We explicitly show that after making use of these modes and by taking into account the quantum metric fluctuation for the problems at hand, the conventional results can indeed be reproduced; but with the advantage of finite answers which require fewer mathematical procedures. An obvious merit of this approach is that the theory is naturally renormalized. The ultraviolet (UV) divergences disappear due to the presence of negative norm state, similar to the Pauli–Villars regularization method. We compare the answers of Krein regularization with the results of calculations which have been done in Hilbert space.

EULER–HEISENBERG LAGRANGIAN THROUGH KREIN REGULARIZATION

The Euler–Heisenberg effective action at the one-loop for a constant electromagnetic field is derived in Krein space quantization with Ford's idea of fluctuated light-cone. In this work, we present a perturbative but convergent solution of the effective action. Without using any renormalization procedure, the result coincides with the famous renormalized Euler–Heisenberg action.