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Speed-of-light pulses in the massless nonlinear Dirac equation with a potential
Niurka R Quintero1, Franz G Mertens2, Fred Cooper3
1Department of Applied Physics, EPS, Virgen de África 7, 41011, Sevilla, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain.
Physical Review. E
|January 20, 2018
Summary
The massless nonlinear Dirac equation with scalar self-interaction exhibits diverse pulse dynamics under external potentials. Final waves are light-speed solutions of the linear Dirac equation, conserving charge and energy.
Area of Science:
- Theoretical physics
- Quantum field theory
- Nonlinear dynamics
Background:
- The massless nonlinear Dirac (NLD) equation describes relativistic quantum phenomena.
- Investigating NLD equations in external potentials is crucial for understanding particle behavior.
Purpose of the Study:
- To analyze the behavior of the massless nonlinear Dirac equation with scalar-scalar self-interaction under various electromagnetic potentials.
- To explore the dynamics of wave propagation, splitting, and focusing.
Main Methods:
- Numerical solutions of the 1+1 dimensional massless NLD equation.
- Analysis of charge, energy, and momentum conservation.
- Derivation of exact analytical solutions for constant potentials.
Main Results:
- Observed pulse propagation, splitting into two opposite-direction pulses, and focusing followed by splitting.
- Final waves consistently travel at the speed of light and solve the linear Dirac equation.
- Charge and energy are conserved; momentum is conserved under specific symmetries.
Conclusions:
- The study reveals rich dynamics of the NLD equation in external potentials.
- The massless NLD equation's solutions transition to linear Dirac equation solutions under specific conditions.
- Potential's imaginary part influences pulse decay or growth, predictable via charge evolution.
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