Plasma-like description for quantum particles

The dispersion relations for the Klein-Gordon equation and a cold collisionless plasma are very similar, but there is another motivation for the plasma-like description of quantum particles. Schrödinger noticed (Nature, 169:538, 1952) that a scalar complex wave function can be made real by a gauge transformation. 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. These results suggest some "symmetry" between positive and negative frequencies and, therefore, particles and antiparticles, so one-particle wave functions can be described as plasma-like collections of numerous particles and antiparticles (A., Eur. Phys. J. C, 73:2371, 2013, Entropy, 24(2):261, 2022).

The criterion for approximation of continuous charge density distributions by discrete ones with quantized charge is their proximity after Gaussian smoothing. Such approximation can be arbitrarily precise (A., arXiv:2503.10667). 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.