Super-energy tensors

A simple and purely algebraic construction of super-energy (s-e) tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena ann-dimensional manifold with a metric of Lorentzian signature. In general, the completely timelike component of these s-e tensors has the mathematical features of an energy density: they are positive definite and satisfy the dominant property, which provides s-e estimates useful for global results and helpful in other matters, such as the causal propagation of the fields. Similarly, super-momentum vectors appear with the mathematical properties of s-e flux vectors. The classical Bel and Bel-Robinson tensors for the gravitational fields are included in our general definition. The energy-momentum and super-energy tensors of physical fields are also obtained, and the procedure will be illustrated by writing down these tensors explicitly for the cases of scalar, electromagnetic, and Proca fields. Moreover, higher order (super)(k)-energy tensors are defined and shown to be meaningful and in agreement for the different physical fields. In Rat spacetimes, they provide infinitely many conserved quantities. In non-flat spacetimes, the fundamental question of the interchange of s-e quantities between different fields is addressed, and answered affirmatively. Conserved s-e currents are found for any minimally coupled scalar field whenever there is a Killing vector. Furthermore, the exchange of gravitational and electromagnetic super-energy is also shown by studying the propagation of discontinuities. This seems to open the door for new types of conservation physical laws.