2007/10/31 by Christian Brouder, Michael Duetsch, Michael Dütsch · 1 citation
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #hep-th
paper · pdf · doi:10.1063/1.2918137
published as J.Math.Phys.49:052303,2008 · The case of gauge fields was added. 16 pages
arxiv created 2008/02/22 · openalex publication_date 2008/05/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 formalisms correctly, a map σ from on-shell fields to off-shell fields was axiomatically introduced by Dütsch and Fredenhagen [Common. Math. Phys. 243, 275 (2003)]. In that paper it is 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 is only recursively given there. We solve this recurrence relation and give a fully explicit expression for σ in the cases of the scalar, Dirac, and gauge fields for arbitrary values of the dimension N.