Arbitrariness of the general solution and symmetries
Results of the author [J. Math. Phys. 35, No. 1, 486-498 (1994; Zbl 0803.35143)] concerning the computation of the number of arbitrary functions in the general solution of a system of involutive PDEs are briefly reviewed. They are used to study normal systems and their symmetry reductions. The computation of the number of physical degrees of freedom in gauge systems and the analysis of gauge fixing conditions are discussed. As examples, the Yang-Mills equations with the Lorentz gauge and Einstein's vacuum field equations with harmonic coordinates are considered.
scientific article; zbMATH DE number 824536