Plasma-like description for quantum particles

Schrödinger noticed (Nature, 169:538, 1952) that a scalar complex wave function can be made real by a gauge transformation. It turned out that one real function is also enough to describe matter in more realistic theories, such as the Dirac equation in an arbitrary electromagnetic (A., J. Math. Phys., 52:082303, 2011, Eur. Phys. J. C, 84:488, 2024) or Yang-Mills (A., Quantum Reports, 4(4):486–508, 2022) field. As these results suggest some "symmetry" between positive and negative frequencies and, therefore, particles and antiparticles, one-particle wave functions can be described as plasma-like collections of a large number of particles and antiparticles (A., Eur. Phys. J. C, 73:2371, 2013, Entropy, 24(2):261, 2022). The similarity of the dispersion relations for the Klein-Gordon equation and a simple plasma model provides another motivation for the plasma-like description of quantum particles.

The criterion for approximation of continuous charge density distributions by discrete ones with quantized charge is the equality of partial Fourier sums. Such approximation can be arbitrarily precise. An example mathematical model of the interpretation and its modification for composite particles are proposed.

Such a description can become at least a basis of an interesting model of quantum mechanics. For example, it can offer an intuitive picture of the uncertainty principle, the double-slit experiment, and negative probabilities. Wave function spreading is not problematic for the model.