Natural Order and Science

[I_am_not_mafia]

Quote mining again, but this time taking more time to mangle the sentences so that they are harder to google.

Infra-red divergences are due to using UNPHYSICAL variables to describe in and out states and introduce gauge invariant, physical “dressed” states. In scattering calculations, it is a common tendency to make an assumption that the coupling constant can be set to zero at infinitely remote times. In QED this might appear reasonable while in QCD such calculations are often based on the premise of some parton-hadron duality. The results of scattering calculations are, though, plagued by infra-red (IR) divergences.

http://pos.sissa.it/archive/conferences/...09_023.pdf

It has long been known that the soft divergences occurring in QED can be cancelled out in transition rates or cross sections computed for detectors with finite energy resolution: the soft divergences which occur in a scattering process due to the emission of an undetected soft real photons with total energy ≤ El exactly cancel out the soft divergences due to virtual photon corrections order by order in perturbation theory. This cancellation was first shown by Bloch and Nordsieck in QED and is referred to as Bloch-Nordsieck theorem. In ordinary (commutative) Yang-Mills theories just as in QED, there exist IR (soft) divergences due to MASSLESS GLUONS. This has been guaranteed by the theorems of Kinoshita and of Lee and Nauenberg known as KLN theorem which states that the transition rates are free of the collinear and soft divergences if we sum over initial and final states. This theorem is a fundamental quantum mechanical theorem on the basis of unitarity of S-matrix.

http://arxiv.org/pdf/hep-th/0609181.pdf
http://pos.sissa.it/archive/conferences/...09_023.pdf

Field theories with space-time non-commutativity, for example, do not have a unitary S-matrix. The extra branch cuts in these theories, are developed in the loop diagrams which are responsible for the failure of the cutting rules and lack of unitary S-matrix.

http://arxiv.org/pdf/hep-th/0005129.pdf

In a scattering process computed up to one-loop order, if we consider the non-commutative soft photon emission, the non-commutative logarithmic IR divergence in the vertex correction will be cancelled in the cross section. However, there are additional non-Abelian type diagrams in which their non-commutative logarithmic and quadratic divergences cannot be cancelled out using the cross section method. This non-cancellation is attributed to an important difference between soft and non-commutative IR divergences. The soft divergences are associated with the classical limit but non-commutative IR divergences are completely a quantum mechanical effect and the soft divergences that only appear in the non-planar vertex correction to be cancelled out in the physical cross section to all orders.

http://arxiv.org/pdf/hep-th/0609181.pdf