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
Fundamental interaction and at long distances the lines of force collimate into strings. In this way, the mathematical theory of QCD not only explains how quarks interact over short distances but also the string-like behavior, discovered by Chew and Frautschi, which they manifest over longer distances. Numerous theoretical efforts have been made to systematize the existing four fundamental interactions on the model of electroweak unification. Grand Unified Theories (GUTs) are proposals to show that the three fundamental interactions described by the Standard Model are all different manifestations of a single interaction with symmetries that break down and create separate interactions below some