Hadronic instabilities in very intense magnetic fields

Composite hadronic states exhibit interesting properties in the presence of very intense magnetic fields, such as those conjectured to exist in the vicinity of certain astrophysical objects. We discuss three scenarios. (i) The presence of vector particles with anomalous magnetic moment couplings to scalar particles, induces an instability of the vacuum. (ii) A delicate interplay between the anomalous magnetic moments of the proton and neutron makes, in magnetic fields B greater-than-or-equal-to 2 x 10(14) T, the neutron stable and for fields B greater-than-or-equal-to 5 X 10(14) T the proton becomes unstable to a decay into a neutron via beta emission. (iii) In the unbroken chiral sigma model magnetic fields would be screened out as in a superconductor. It is the explicit breaking of chiral invariance that restores standard electrodynamics. Astrophysical consequences of all these phenomena are discussed.