Ghost-free infinite derivative quantum field theory

Understand

In this paper we will study Lorentz-invariant, infinite derivative quantum field theories, where infinite derivatives give rise to non-local interactions at the energy scale $M_s$, beyond the Standard Model.

• We will study a specific class, where there are no it new dynamical degrees of freedom other than the original ones of the corresponding local theory.
• We will show that the Green functions are modified by a non-local extra term that is responsible for acausal effects, which are confined in the region of non-locality, i.e.
• $M_s^{-1}.$ The standard time-ordered structure of the causal Feynman propagator is not preserved and the non-local analog of the retarded Green function turns out to be non-vanishing for space-like separations.