Tachyonic equations to reduce the divergent integral of QED

TL;DR

This paper proposes a tachyonic equation approach to address divergence issues in QED integrals, validated through Cherenkov radiation analogies, and successfully applied to compute the Lamb shift without a cutoff frequency.

Contribution

It introduces a novel tachyonic equation framework that reduces divergence in QED calculations and eliminates the need for a cutoff frequency in Lamb shift computations.

Findings

Divergence in QED integrals can be mitigated using tachyonic equations.

Cherenkov radiation analog confirms the tachyonic formulation.

Lamb shift calculated without a cutoff frequency.

Abstract

If the total integral including both 0<V<c and c<V<infinity is considered, divergence will be reduced.Firstly,we use the Cherenkov radiation in media as analogue to confirm the formulation (7)-(10) of a tachyon in vacuum.Then these equations are applied to calculate the Lamb shift and the cut-off frequency is unnecessary.