  Inspired by classical work of Bel and Robinson, a natural purely algebraic
construction of super-energy tensors for arbitrary fields is presented, having
good mathematical and physical properties. Remarkably, there appear quantities
with mathematical characteristics of energy densities satisfying the dominant
property, which provides super-energy estimates useful for global results and
helpful in other matters. For physical fields, higher order (super)^n-energy
tensors involving the field and its derivatives arise. In Special Relativity,
they provide infinitely many conserved quantities. The interchange of
super-energy between different fields is shown. The discontinuity propagation
law in Einstein-Maxwell fields is related to super-energy tensors, providing
quantities conserved along null hypersurfaces. Finally, conserved super-energy
currents are found for any minimally coupled scalar field whenever there is a
Killing vector.
