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

TL;DR

This paper extends the Hamiltonian approach to a broad class of ultraviolet finite non-local quantum field theories inspired by quantum gravity, proving the existence of the weak adiabatic limit for these theories.

Contribution

It generalizes the Hamiltonian quantization method to non-local theories inspired by quantum spacetime, establishing foundational properties and the weak adiabatic limit.

Findings

Proved the existence of the weak adiabatic limit for the class of theories.

Discussed general properties of ultraviolet finite non-local quantum field theories.

Extended Hamiltonian approach to non-local effective theories.

Abstract

The non-local quantum field theories attract interest in the mathematical and physical community as candidates for effective description of the reality taking into account the quantum gravity effects. The standard methods, developed for the conventional local quantum field theories, often are not applicable. In this paper the Hamiltonian approach, originally proposed for quantization of the non-local effective theory inspired by non-commutative geometry of the Doplicher-Fredenhagen-Roberts Quantum Spacetime, is generalized to a large class of ultraviolet finite non-local Hamiltonian perturbative Quantum Field Theories. General properties of such theories are discussed. The weak adiabatic limit existence is proved for the whole class of theories.