Plasma-like Description for Elementary and Composite Quantum Particles

Area of Science:

• Quantum Mechanics
• Theoretical Physics
• Mathematical Physics

Background:

• Schrödinger's 1952 observation on real wave functions via gauge transformation.
• Recent work showing a single real function suffices for Dirac equation in complex fields.
• Hypothesized symmetry between positive/negative frequencies, particles/antiparticles.

Purpose of the Study:

• To propose a quantum mechanical model describing particles and antiparticles using real wave functions.
• To develop a criterion for approximating continuous charge distributions with discrete, quantized charges.
• To extend this model to composite particles.

Main Methods:

• Utilizing gauge transformations to simplify wave functions.
• Applying the homotopy continuation method for approximation.
• Developing a mathematical model for the proposed description.

Main Results:

• A criterion for approximating continuous charge density distributions by discrete, quantized ones.
• Successful computation of an example approximation using the homotopy continuation method.
• Extension of the model to describe composite particles as collections of particles and antiparticles.

Conclusions:

• The proposed model offers a potentially useful picture of quantum mechanics, though its physical reality requires further investigation.
• The model provides a basis for interesting theoretical explorations in quantum mechanics.
• The approach highlights a potential symmetry between particles and antiparticles in quantum field descriptions.