Abstract
A new form of the light front Feynman propagators is proposed. It contains no energy denominators. Instead the dependence on the longitudinal subinterval \(x^2_L = 2 x^{+} x^{-}\) is explicit and a new formalism for doing the perturbative calculations is invented. These novel propagators are implemented for the one-loop effective potential and various 1-loop 2-point functions for a massive scalar field. The consistency with results for the standard covariant Feynman diagrams is obtained and no spurious singularities are encountered at all. Some remarks on the calculations with fermion and gauge fields in QED and QCD are added.
Highlights
Wightman function for a free massive scalar field 0|φ(x)φ(0)|0 = W2(x) has its LF momentum representation W2(x+, x−, x⊥) =d 2 k⊥ (2π )2 e−i k⊥· x ⊥ ∞ dk+ 4π k+ e−i k + x − e−i m 2 +k2⊥ 2k+ x+ (1)
This expression gives nontrivial contribution to the effective potential, which can be compared with the result obtained within the standard LF formulation [4]
We may consider the 2-point function, which has been used by Melikhov and Simula in [5] for their discussion of spurious end-point singularities
Summary
For k+ → 0, the pole in k− moves to infinity, so the naive implementation of the residua theorem can lead to false results. This problem overlaps with the usual LF singularity due to 1/k+ pole. The very trick, presented in (4), is analogous to the equal-time propagators, where one makes the ordering in x0 temporal variable, so one introduces. In this calculation the shifting of k0 is reliable since the limit ωk → ∞ is suppressed by the inverse power of ωk in the invariant measure factor, on contrary in the Eq (4). It is not strange that the LF propagator with the pole structure as in (4) may lead to various artificial singularities of Feynman diagrams, which are absent in the analogous equal-time calculation
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