Resolutions of the Infrared Divergence in Qft

Though QFT is well developed and successful in theoretical aspects and applications, there are some defects in QFT [1]. Ultraviolet divergences and infrared divergences are serious defects of QFT. The ultraviolet divergence will not be discussed in this article since it was discussed by Hung-Ming Tsai et al. in 2003 [2]. There are two approaches to remove the infrared singularities. The first part of this article is the mathematical proof of the existence of a positive lower bound of the energy of emitted photons or gluons. Therefore, the soft divergence is removed. The second part of this article is to show the existence of a regular basis of the solution space of the field equation. The second quantization is based on this regular basis. With this regular basis, the infrared divergences, both the soft divergence and the collinear divergence, are expected to be removed.