Relating on-shell and off-shell formalism in perturbative quantum field theory
نویسندگان
چکیده
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 onand off-shell formalism correctly, a map σ from on-shell fields to off-shell fields was introduced axiomatically in [1]. 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 given there only recursively. We solve this recurrence relation and give a fully explicit expression for σ in the cases of the scalar and Dirac field for arbitary values of the dimension N .
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