Physic Labs

Particle physics

The Dirac field and fermions

Observe the Dirac field and fermion current in three dimensions. Check the conserved current jμ=ψˉγμψj^\mu = \bar\psi\gamma^\mu\psi, ∂μjμ=0\partial_\mu j^\mu = 0 via the field's flow pattern as strength and energy scale vary.

Research

Equipment

  • 3D view of the Dirac field / fermion
  • Sliders for strength and energy scale
  • Pause and reset-view buttons

Procedure

  1. Survey the field structure

    Rotate the 3D view (drag) to see the Dirac field from several directions; note the vortex-like streamlines representing the fermion current jμ=ψˉγμψj^\mu = \bar\psi\gamma^\mu\psi. Read the readout for the current strength value.

  2. Vary strength and scale

    Drag the "Strength" and "Energy scale" sliders and watch the density and curvature of streamlines change. Press "Pause" at a few settings to check: streamlines have no free sources or sinks — illustrating ∂μjμ=0\partial_\mu j^\mu = 0, like incompressible flow.

  3. Compare with the Dirac equation

    Recall the equation (iγμ∂μ−m)ψ=0(i\gamma^\mu\partial_\mu - m)\psi = 0: changing "Energy scale" alters the relative role of mm versus momentum. Note the spinor ψ has 4 components (particle + antiparticle, spin up/down); press "Reset view" and repeat the observation at another setting to check that the current's structure stays conserved.

Simulation

Experiment history

In 1928 Paul Dirac sought a wave equation both relativistic and first-order in time, arriving at (iγμ∂μ−m)ψ=0(i\gamma^\mu\partial_\mu - m)\psi = 0 — where γμ\gamma^\mu are 4×4 matrices. The equation automatically predicts spin 1/2 and the electron's gyromagnetic ratio g=2g = 2, and it forces the existence of negative-energy states that Dirac reinterpreted as "antiparticles". In 1932 Carl Anderson discovered the positron in cosmic rays, confirming the prediction. In later quantum field theory, ψ became a field operator creating and annihilating fermions; the current jμ=ψˉγμψj^\mu = \bar\psi\gamma^\mu\psi is the source coupling to photons in quantum electrodynamics (QED), completed by Feynman, Schwinger, and Tomonaga in the late 1940s.

Related physicists

Paul DiracRichard FeynmanCarl David Anderson

Related library topics

The Dirac field and fermions