Exchange interaction independently by physicists Werner Heisenberg and Paul Dirac in 1926. The exchange interaction is sometimes called the "exchange force". However, it is not a true force and should not be confused with the exchange forces produced by the exchange of force carriers, such as the electromagnetic force produced between two electrons by the exchange of a photon, or the strong force between two quarks produced by the exchange of a gluon. Although sometimes erroneously described as a force, the exchange interaction is a purely quantum mechanical "effect" unlike other forces. Quantum mechanical particles are classified as bosons or fermions. The
Gauge theory are included in the Lagrangian to ensure its invariance under the local group transformations (called "gauge invariance"). When such a theory is quantized, the quanta of the gauge fields are called "gauge bosons". If the symmetry group is non-commutative, then the gauge theory is referred to as non-abelian gauge theory, the usual example being the Yang–Mills theory. Many powerful theories in physics are described by Lagrangians that are invariant under some symmetry transformation groups. When they are invariant under a transformation identically performed at "every" point in the spacetime in which the physical processes occur, they are said to have