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The non-local quantum field theories attract interest in the mathematical andphysical community as candidates for effective description of the realitytaking into account the quantum gravity effects. The standard methods,developed for the conventional local quantum field theories, often are notapplicable. In this paper the Hamiltonian approach, originally proposed forquantization of the non-local effective theory inspired by non-commutativegeometry of the Doplicher-Fredenhagen-Roberts Quantum Spacetime, is generalizedto a large class of ultraviolet finite non-local Hamiltonian perturbativeQuantum Field Theories. General properties of such theories are discussed. Theweak adiabatic limit existence is proved for the whole class of theories.

Ultraviolet finite non-local Hamiltonian perturbation Quantum Field Theories and their weak adiabatic limit