Relating on-shell and off-shell formalism in perturbative quantum field theory

Details Relating on-shell and off-shell formalism in perturbative quantum field theory Relating on-shell and off-shell formalism in perturbative quantum field theory

2007-10-16

arxiv.org/abs/0710.3040v2

J.Math.Phys.49:052303,2008

Physics

High Energy Physics

High Energy Physics - Theory

The case of gauge fields was added. 16 pages

Scientific paper

10.1063/1.2918137

In the on-shell formalism (mostly used in perturbative quantum field theory) the entries of the time ordered product T are on-shell fields (i.e. the basic fields satisfy the free field equations). With that, (multi)linearity of T is incompatible with the Action Ward identity. This can be circumvented by using the off-shell formalism in which the entries of T are off-shell fields. To relate on- and off-shell formalism correctly, a map sigma from on-shell fields to off-shell fields was introduced axiomatically by Duetsch and Fredenhagen. In that paper it was shown that, in the case of one real scalar field in N=4 dimensional Minkowski space, these axioms have a unique solution. However, this solution was given there only recursively. We solve this recurrence relation and give a fully explicit expression for sigma in the cases of the scalar, Dirac and gauge fields for arbitrary values of the dimension N.

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