A tentative plasma-like interpretation of elementary and composite particles in quantum theory

Schrödinger noticed in 1952 that a scalar complex wave function can be made real by a gauge transformation. It was shown recently that one real function is also enough to describe matter in more realistic theories, such as the Dirac equation in an arbitrary electromagnetic or Yang-Mills field. As these results suggest some "symmetry" between positive and negative frequencies and, therefore, particles and antiparticles, the author previously considered an interpretation of one-particle wave functions as plasma-like collections of a large number of particles and antiparticles. This work offers a criterion for approximation of continuous charge density distributions by discrete ones with quantized charge based on the equality of partial Fourier sums. An example of such approximation is computed using the homotopy continuation method. An example mathematical model of the interpretation is proposed. A modification of the interpretation for composite particles, such as nucleons or large molecules, describes them as collections including a composite particle and a large number of pairs of elementary particles and antiparticles. While it is not clear if such an interpretation describes the reality correctly, it can become a basis of an interesting model of quantum mechanics.