Playground 05
Left-Handed vs Right-Handed Spinors
Track left and right chiral components under boosts, then watch a mass term tie them together into one Dirac spinor.
Animation Controls
Current build step
1. Chiral sectors separated
0%
rest framemoderatestrong
masslessmixedstrongly coupled
left-leaningbalancedright-leaning
Left sector
1.38x
Right sector
0.75x
Mass bridge
waiting
Chirality Construction
Two chiral pieces, one Dirac field
The left and right sectors transform differently under boosts, and the mass term is what ties them into one massive fermion.
Chirality map
Chiral split
Before adding mass, the left and right sectors can be treated separately and transform as distinct ingredients.
Left piece
Right piece
Combination
Mass coupling
The mass term is the bridge that talks between both chiral sectors, which is why a massive Dirac fermion needs both pieces.
Mass term
Coupling strength
0.08
Massless limit
bridge remains
What to notice
The left and right pieces are not just cosmetic labels. They really respond differently, which is why the separate panels help before combining them.
Why mass matters
In the massless limit, the chiral sectors stop talking to each other. Turning on mass creates the bridge that makes a full Dirac fermion feel constructed rather than mysterious.
Try this
Pull mass coupling toward zero and watch the bridge fade. Then raise it again to see the Dirac construction become a visibly linked two-sector system.