QED in Krein Space Quantization

Abstract

In this paper we consider the QED in Krein space quantization. We show that the theory is automatically regularized. The three primitive divergences integrals in usual QED are considered in Krein QED. The photon self energy, electron self energy and vertex function are calculated in this formalism. We show that these quantities are finite. The infrared and ultraviolet divergencies do not appear. We discuss that Krein space quantization is similar to Pauli-Villars regularization, so we have called it the "Krein regularization".

QED effective action in Krein space quantization

“…Now, one compares this result with standard solution Eq. (A.7).This new kind of regularization may be utilized in the calculation of the Lamb-Shift and Magnetic-Anomaly[16].…”

A brief review on the problem of divergence in Krein space quantization

“…where q 2 = (p − p ′ ) 2 . The singular terms of 3 standard graphs of QED are replaced with the two first terms in the resulted graphs in Krein space quantization [24,25]. By using the value of F 1 (q 2 ) and the photon self energy in Krein space, the value of Lamb Shift is calculated to be 1018.…”

Krein Regularization of λϕ 4

“…The tree order S-matrix elements do not change because the propagator in the two methods is the same (k 2 = m 2 ) [12].…”

“…It has been shown that the Krein propagators which obey the Krein quantization and quantum metric fluctuation are finite [10][11][12][13]. The most interesting result of this construction is a new method of regularization, which we have called "Krein regularization".…”