One example of a field theory that is not electromagnetism is quantum field theory (QFT). Quantum field theory is a theoretical framework that combines elements of quantum mechanics and special relativity to describe the behavior of elementary particles and their interactions.
In quantum field theory, fields are considered fundamental entities that permeate all of space and time. These fields are quantized, meaning that they are composed of discrete units or quanta, which are particles. The interactions between these particles are described by mathematical objects called Feynman diagrams.
Quantum field theory provides a framework for understanding and calculating a wide range of phenomena in particle physics, such as the behavior of elementary particles, the creation and annihilation of particles, and the scattering of particles during interactions. It has been successful in predicting and explaining a variety of experimental results.
It is important to note that quantum field theory is a broad framework that encompasses various specific field theories, such as the Standard Model of particle physics, which describes the electromagnetic, weak, and strong nuclear interactions. So while QFT itself is not electromagnetism, it can incorporate electromagnetism as one aspect within its larger framework.