General relativity (GR) and quantum field theory (QFT) are two of the most successful and well-tested theories in physics. However, combining them to provide a complete and consistent description of gravitation at the quantum level has proven to be a significant challenge.
In the framework of classical general relativity, gravity is described as the curvature of spacetime caused by the distribution of mass and energy. It provides a successful description of gravity on large scales, such as the motion of planets, the behavior of stars, and the expansion of the universe. However, at the quantum level, the theory encounters several conceptual and mathematical difficulties, primarily due to the nonrenormalizability of the theory.
On the other hand, quantum field theory is a powerful framework for describing the behavior of particles and forces in the context of quantum mechanics. It successfully describes the electromagnetic, weak, and strong nuclear forces, which are mediated by the exchange of particles called gauge bosons. However, when attempting to include gravity in the framework of QFT, fundamental issues arise. Gravitational interactions are mediated by a spin-2 particle called the graviton, and the coupling of a massless spin-2 particle to matter fields in a consistent way is difficult to achieve within the standard QFT framework.
Efforts to combine general relativity and quantum field theory have led to various approaches, such as string theory, loop quantum gravity, and other quantum gravity models. These attempts aim to provide a quantum theory of gravity that encompasses both GR and QFT and resolves the challenges that arise from their combination. However, these theories are still areas of active research and remain incomplete and speculative.
In summary, while general relativity and quantum field theory are highly successful theories in their respective domains, combining them to explain gravitation at the quantum level is still an open problem. The quest for a complete theory of quantum gravity that unifies GR and QFT is an ongoing pursuit in theoretical physics.