Quantum Field Theory (QFT) describes the interactions of the Standard Model, except for gravity, in a very precise manner. QFT rests on the principles of Quantum Theory and Special Relativity. In this framework, particles and interactions evolve according to their equations of motion as quantized fields on a given 4-dimensional spacetime-manifold. The metric tensor field of gravitation determines spacetime, which can be curved in general.
Experiments show the validity and applicability of QFT for a wide range of energy scales. For example, in 2012 the researchers at the CERN in Geneva were able to detect the Higgs-particle, which is one of the basic constituents of the Standard Model.
However, QFT by itself has its problem, because to date in four dimensions only a perturbative description of interacting quantum matter is available. Moreover, the individual terms in the perturbation series diverge and can be made finite only by subtracting the divergencies in a procedure called renormalisation. Further problems occur when high energy densities play a role, in which case the gravitational field can no longer be assumed to behave classically. This however, is a main ingredient for the theory of quantum fields based on the Wightman axioms.