On the Arbitrariness of the General Solution of an Involutive Partial Differential Equation

Reference: Journal of Mathematical Physics, 35 (1994) 486-498

Description: This was my first paper on the formal theory of differential equations. It considers the problem of determining the number of arbitrary functions in the general solution of an involutive system. Studying this problem helped me a lot understanding the meaning of the Cartan characters and of the Hilbert polynomial. However, one must be very careful when the results are applicable and I was not careful enough when I wrote that paper. Especially the distinction between algebraic and integral representation of the general solution is not really correct. Of more importance and interest are the comparison with Einstein's strength and the results on gauge symmetries. These topics have been taken up again in [7, 17] . Especially, the latter paper presents a more elegant approach using Lie pseudogroups.

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