Classical unified field theories since antisymmetry seemed essential for electromagnetism, the symmetry requirement was relaxed for one or both fields. Einstein's proposed unified-field equations (fundamental laws of physics) were generally derived from a variational principle expressed in terms of the Riemann curvature tensor for the presumed space-time manifold. In field theories of this kind, particles appear as limited regions in space-time in which the field strength or the energy density are particularly high. Einstein and coworker Leopold Infeld managed to demonstrate that, in Einstein's final theory of the unified field, true singularities of the field did have trajectories resembling point particles. However, singularities are
Unified field theory formula_7 manifold. In mathematics, if f(z) is a holomorphic function restricted to the Real Numbers, it has the complex conjugate properties of f (z) = f *(z*), which leads to the above equation when formula_21 is satisfied. All four of the known fundamental forces are mediated by fields, which in the Standard Model of particle physics result from exchange of gauge bosons. Specifically the four fundamental interactions to be unified are: Modern unified field theory attempts to bring these four interactions together into a single framework. The first successful classical unified field theory was developed by James Clerk Maxwell. In