Equivalence of light-front and covariant field theory

Abstract

In this paper we discuss the relation between the standard covariant quantum field theory and light-front field theory. We define covariant theory by its Feynman diagrams, whereas light-front field theory is defined in terms of light-cone time-ordered diagrams. A general algorithm is proposed that produces the latter from any Feynman diagram. The procedure is illustrated in several cases. Technical problems that occur in the light-front formulation and have no counterpart in the covariant formulation are identified and solved. The problem of renormalization is not discussed in this paper.

Light-Front Singularities

“…The tadpoles, which are necessarily singular because of the arc contributions, are in Ref. [10] found to be…”

“…The last integral can be evaluated in a straightforward way integrating over k − first and using the residue theorem The two integrals with a single denominator, tadpoles, can be treated using a method pioneered by Ligterink and Bakker [10]. In the latter work a method invented by Yan [11] was utilized.…”

“…[10]. The LF amplitude with blinks is obtained adding the amplitude with an instantaneous fermion propagator to the amplitude with LF fermion propagators.…”

Box diagram in Yukawa theory

“…If we combine the LF-propagating and instantaneous parts to blinks [19], the longitudinal singularities cancel out. It is easy to show that the open diamond is obtained by integrating a function that is finite in domain 3.…”

“…Diagrams (a) and (b) correspond to region 2, diagrams (c), (d), (e), (f), and (g ) correspond to region 3 and diagrams (h) and (i) correspond to region 4. We can decrease the number of diagrams we have to use with the blink mechanism [19], which we will do for each region.…”