NONLOCAL GENERALIZED ANGULAR-MOMENTUM BALANCE LAWS AND EQUATIONS OF MOTION

It is shown how systems of nonlocal (i.e. integrodifferential) linear second-order equations of motion (LSIDEs) can be directly related to associated nonlocal angular-momentum complexes as well as to balance laws corresponding to such complexes. This gives one the freedom to obtain balance laws from given LSIDEs or vice versa. These laws will, as usual, augment the equations of motion as further useful information about the physical system. Under certain conditions one then sees how the balance laws reduce to corresponding conservation laws. Two examples, sketched to indicate bow the formalism can be applied, come from continuum mechanics and quantum mechanics for physical systems described by nonlocal interactions. A third example is from quantum field theory for the case of local interactions for particles of arbitrary integral spin in general, and for electromagnetism in particular. The formalism can thus be appled to physical systems whose equations of motion may be relativistic and either classical or quantum mechanical.