Non-unitarity of Minkowskian non-local quantum field theories

Abstract

We show that Minkowskian non-local quantum field theories are not unitary. We consider a simple one loop diagram for a scalar non-local field and show that the imaginary part of the corresponding complex amplitude is not given by Cutkosky rules, indeed this diagram violates the unitarity condition. We compare this result with the case of an Euclidean non-local scalar field, that has been shown to satisfy the Cutkosky rules, and we clearly identify the reason of the breaking of unitarity of the Minkowskian theory.

References in corpus (15)

• Route to nonlocal cosmology
• Exacting N=4 Superconformal Symmetry
• Inflation in (Super-)renormalizable Gravity
• Nonlocal quantum gravity and M-theory
• Generalized ghost-free propagators in nonlocal field theories
• Nonlinear stability in nonlocal gravity
• Unitarity of Minkowski non-local theories made explicit
• Non-Gaussianities and tensor-to-scalar ratio in non-local $R^2$-like inflation
• One-loop beta-functions for renormalisable gravity
• Probing the vacuum fluctuations in scalar ghost-free theories
• Angle deficit & non-local gravitoelectromagnetism around a slowly spinning cosmic string
• Unattainability of the Trans-Planckian regime in Nonlocal Quantum Gravity
• On thermal field fluctuations in ghost-free theories
• Hidden Non-Locality and Self-Superrenormalization of Quantum Gravity
• Effects of Non-locality in Gravity and Quantum Theory

Cited by in corpus (17)

• On the contour prescriptions in string-inspired nonlocal field theories
• Quantum field theory with ghost pairs
• Asymptotic nonlocality in non-Abelian gauge theories
• Quintessence Dark Energy from strongly-coupled Higgs mass gap: Local and Non-local higher-derivative non-perturbative scenarios
• Early universe in quantum gravity
• Asymptotic nonlocality in gauge theories
• Asymptotic nonlocality
• Path integral and conformal instability in nonlocal quantum gravity
• Stringballs and Planckballs for Dark Matter
• Non-perturbative Lee-Wick gauge theory: Towards Confinement and RGE with strong couplings
• Fate of the false vacuum in string-inspired nonlocal field theory
• Quantum avoidance of Gödel's closed timelike curves
• The Weinberg no-go theorem for cosmological constant and nonlocal gravity
• Nonlocal Spacetime-Matter
• Towards Hamiltonian Formalism for String Field Theory and Nonlocality
• Acausal exact vacuum solutions in nonlocal gravity
• Renormalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance