Relativistic Wave Equations

Investigate relativistic wave equations, energy sectors, current and controlled nonrelativistic limits. One-particle wave mixing does not by itself measure field-theoretic particle creation.

Choose an investigation

• Lorentz Transformations — Run finite boosts, rotations, exact rational fixtures, and an independent mass-shell Jacobian check while tracking high-rapidity loss of floating-point accuracy.
• Klein–Gordon Wave Packets — Evolve both Klein–Gordon Cauchy data with exact Fourier modes, distinguish signed charge from field intensity, and independently test box size, cutoff, and nonrelativistic errors.
• Dirac Wave Packets — Evolve free Dirac packets by exact Fourier modes, separate energy sectors from spinor components, and compare coherent current oscillations, dephased mixtures, and controlled position diagnostics.
• Spinor Algebra — Execute Clifford, spin-sum, polarization, and discrete-map checks in three spinor bases, with exact fixtures and explicit floating-point error scales.
• Foldy–Wouthuysen Expansion — Verify static Foldy–Wouthuysen coefficients with ordered exact algebra, polynomial electromagnetic fixtures, matrix exponentials, and controlled square-root remainders.
• Relativistic Landau Levels — Diagonalize the oscillator-basis Dirac Hamiltonian, recover physical Landau multiplicities with projectors, and expose persistent cutoff artifacts.
• Klein Paradox — Match stationary Dirac step modes, choose outgoing channels by current, and verify reflection and transmission across propagating, evanescent, and Klein regions.
• Mott Scattering — Verify fixed-source Mott scattering with explicit spinors and independent traces, compare angular spin factors, and separate quadrature convergence from the forward Coulomb divergence.
• Propagator Visualization Notebook — Compare unit-source retarded, advanced, and Feynman scalar mode kernels through compact-source responses, independent ODE checks, and separate regulator limits.

Interpret the evidence

The Labs catalog distinguishes downloadable pilot packages from other existing script-backed investigations. Each investigation states its own assumptions and retained checks. Follow Running an Experiment for the shared execution workflow and the Reproducibility Checklist for evidence and error budgets.

References

• National Academies of Sciences, Engineering, and Medicine, Reproducibility and Replicability in Science, National Academies Press, 2019, doi:10.17226/25303 — interpreting reproducibility and independent scientific evidence.