Non-unitarity of Minkowskian non-local quantum field theories
Fabio Briscese, Leonardo Modesto
Abstract
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.
Topics & Concepts
UnitarityUnitary stateEuclidean geometryQuantum field theoryPhysicsScalar (mathematics)Theoretical physicsScalar fieldField (mathematics)Field theory (psychology)QuantumMathematical physicsQuantum mechanicsMathematicsPure mathematicsGeometryLawPolitical scienceCosmology and Gravitation TheoriesNoncommutative and Quantum Gravity TheoriesQuantum Electrodynamics and Casimir Effect