for real or complex scalar fields Dirac theory for a Dirac spinor field Yang–Mills theory for a non-abelian gauge field Unification attempts Attempts to create a unified field theory based on classical physics are classical unified field theories. During the years between the two World Wars, the idea of unification of gravity with electromagnetism was actively pursued by several mathematicians and physicists like Albert Einstein, Theodor Kaluza, Hermann Weyl, Arthur Eddington, Gustav Mie and Ernst Reichenbacher. Early attempts to create such theory were based on incorporation of electromagnetic fields into the geometry of general relativity. In 1918, the case for the first geometrization of the electromagnetic field was proposed in 1918 by Hermann Weyl. In 1919, the idea of a five-dimensional approach was suggested by Theodor Kaluza. From that, a theory called Kaluza-Klein Theory was developed. It attempts to unify gravitation and electromagnetism, in a five-dimensional space-time. There are several ways of extending the representational framework for a unified field theory which have been considered by Einstein and other researchers. These extensions in general are based in two options. The first option is based in relaxing the conditions imposed on the original formulation, and the second is based in introducing other mathematical objects into the theory. An example of the first option is relaxing the restrictions to four-dimensional space-time by considering higher-dimensional representations. That is used in Kaluza-Klein Theory. For the second, the most prominent example arises from the concept of the affine connection that was introduced into the theory of general relativity mainly through the work of Tullio Levi-Civita and Hermann Weyl. Further development of quantum field theory changed the focus of searching for unified field theory from classical to quantum description. Because of that, many theoretical physicists gave up looking for a classical unified field theory. Quantum field theory would include unification of two other fundamental forces of nature, the strong and weak nuclear force which act on the subatomic level. See also Relativistic wave equations Quantum field theory Classical unified field theories Variational methods in general relativity Higgs field (classical) Lagrangian (field theory) Hamiltonian field theory Covariant Hamiltonian field theory Notes References Citations Sources External links Mathematical physics Theoretical physics Lagrangian mechanics Equations