A critical review is given of the main theoretical bases and of the experimental results of neutrino physics at low four-momentum transfer (Q2≤1 GeV 2) and high energy transfer (ν≥a few GeV). The theoretical predictions for the vector current are first presented, using the CVC hypothesis and the hadron dominance model of Piketty and Stodolsky. The predictions for the axial current at very small Q2 values are discussed on the basis of the PCAC hypothesis (Adler’s theorem), and extended for Q2≲1 GeV 2 in the lines of hadron dominance; the structure of the longitudinal component of the axial current is particularly discussed. Experimental data on neutrino and antineutrino interactions on nucleons are reviewed, in particular the total cross sections, which provide good tests of the PCAC hypothesis and of the model of Piketty and Stodolsky; also reviewed are the data on diffractive production of π, ρ and a1 mesons. The observation of shadowing, from the comparison of the total cross sections of neutrinos and antineutrinos on neon and deuterium nuclei, is discussed in detail with emphasis on the predictions of the PCAC hypothesis, in the framework of the Glauber-Gribov model. Finally a review is given of the results on coherent neutrino and antineutrino interactions on atomic nuclei: • π meson production, by charged and neutral currents in several experiments, providing a detailed test of the PCAC hypothesis; • ρ meson production, providing a test of the CVC hypothesis in weak interactions; • a1 meson or nonresonant ρπ system production, allowing the study of the weak axial current structure.
High-energy behaviour of the transition probabilities and total cross sections for charge exchange