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Gauge invariance is the basis of the modern theory of electroweak and strong interactions (the so called Standard Model). The roots of gauge invariance go back to the year 1820 when electromagnetism was discovered and the first electrodynamic theory was proposed. Subsequent developments led to the discovery that different forms of the vector potential result in the same observable forces. The partial arbitrariness of the vector potential A brought forth various restrictions on it. div A = 0 was proposed by J. C. Maxwell; 4-div A = 0 was proposed L. V. Lorenz in the middle of 1860's . In most of the modern texts the latter condition is attributed to H. A. Lorentz, who half a century later was one of the key figures in the final formulation of classical electrodynamics. In 1926 a relativistic quantum-mechanical equation for charged spinless particles was formulated by E. Schrodinger, O. Klein, and V. Fock. The latter discovered that this equation is invariant with respect to multiplication of the wave function by a phase factor exp(ieX/hc) with the accompanying additions to the scalar potential of -dX/cdt and to the vector potential of grad X. In 1929 H. Weyl proclaimed this invariance as a general principle and called it Eichinvarianz in German and gauge invariance in English. The present era of non-abelian gauge theories started in 1954 with the paper by C. N. Yang and R. L. Mills.Comment: final-final, 34 pages, 1 figure, 106 references (one added with footnote since v.2); to appear in July 2001 Rev. Mod. Phy

The observation of neutrons turning into antineutrons would constitute a discovery of fundamental importance for particle physics and cosmology. Observing the n−n transition would show that baryon number (B) is violated by two units and that matter containing neutrons is unstable. It would provide a clue to how the matter in our universe might have evolved from the B = 0 early universe. If seen at rates observable in foreseeable next-generation experiments, it might well help us understand the observed baryon asymmetry of the universe. A demonstration of the violation of B − L by 2 units would have a profound impact on our understanding of phenomena beyond the Standard Model of particle physics.Slow neutrons have kinetic energies of a few meV. By exploiting new slow neutron sources and optics technology developed for materials research, an optimized search for oscillations using free neutrons from a slow neutron moderator could improve existing limits on the free oscillation probability by at least three orders of magnitude. Such an experiment would deliver a slow neutron beam through a magnetically-shielded vacuum chamber to a thin annihilation target surrounded by a low-background antineutron annihilation detector. Antineutron annihilation in a target downstream of a free neutron beam is such a spectacular experimental signature that an essentially background-free search is possible. An authentic positive signal can be extinguished by a very small change in the ambient magnetic field in such an experiment. It is also possible to improve the sensitivity of neutron oscillation searches in nuclei using large underground detectors built mainly to search for proton decay and detect neutrinos. This paper summarizes the relevant theoretical developments, outlines some ideas to improve experimental searches for free neutron oscillations, and suggests avenues both for theoretical investigation and for future improvement in the experimental sensitivity.

The existence of extra chiral generations with all fermions heavier than M_Z is strongly disfavoured by the precision electroweak data. However the data are fitted nicely even by a few extra generations, if one allows neutral leptons to have masses close to 50 GeV. The data allow inclusion of one additional generation of heavy fermions in SUSY extension of Standard Model if chargino and neutralino have masses close to 60 GeV with \Delta m =~ 1 GeV.Comment: 14 pages, 5 figure