Syzygies and Conservation Laws
We show how the notion of syzygies of a system of partial differential equations allows to derive some conservation laws, for the case of Maxwell and Proca systems. More in general, we apply some classical tools in algebraic analysis to derive properties of the solutions of the previous systems like their integral representations.
Colombo, F., Sabadini, I., Sommen, F., & Struppa, D. C. (2002). Syzygies and conservation laws. Foundations of Physics Letters, 15(6), 507-522. doi: 10.1023/A:1023961018271