Relating on-shell and off-shell formalism in perturbative quantum field theory
arXiv:0710.3040 · doi:10.1063/1.2918137
Abstract
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.
The case of gauge fields was added. 16 pages
References in corpus (10)
- Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
- Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
- Are Nonrenormalizable Gauge Theories Renormalizable?
- Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity
- Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion
- The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory
- Removal of violations of the Master Ward Identity in perturbative QFT
- The Master Ward Identity
- The Wess Zumino consistency condition: a paradigm in renormalized perturbation theory
- Renormalization Group Treatment of Nonrenormalizable Interactions