The quantum physical origin of the gauge idea

To consider quantum physics as an interplay of creation and annihilation processes has the consequence that gauge field theories are not only possible but necessary. Since the complex conjugate phase factors of each pair of fermion creators and annihilators can be arbitrary chosen, quantum field theories must be completely phase invariant. Unfortunately, even globally the Dirac equation for systems of free fermions is not phase invariant. The Dirac matrices change when the spinor components are multiplied by different constant phase factors. The Dirac equations before and after the transformation are however physically equivalent. Systems of free fermions will be completely described, only if the class of all equivalent Dirac equations is considered. Since Dirac's commutation relations are unitarily invariant, the class of equivalent Dirac equations is invariant under all transformations of the group U4. Unitary diagonal matrices yield arbitrary phase transformations. Hence, gauge fields of the group U4 are compatible with the postulate of general phase invariance. The gauge fields are so similar to QED that we may speak of an 'extended quantum electrodynamics', EQE. The invariant subgroup U1 of U4 yields QED. The complementary subgroup SU4 includes 4 subgroups SU3, 3 subgroups O4, and 6 subgroups SU2. The latter ones may yield three pairs of quarks and three pairs of leptons, where the quarks form a group SU3. More than twice three pairs of elementary fermions does not exist in EQE. Probably, EQE is different from the united QED and QCD. However, it should be a promising version of a field theory in elementary particle physics. (author)