= Neveu–Schwarz Fourier phase-space action
{c}
{title2=$S=\int(\dot x\cdot p+\sum_{k>0}i\alpha_{-k}\dot\alpha_k/k+i\sum_{r>0}b_{-r}\dot b_r-\lambda L-i\chi G)\,dt$}
The open NS action has integer bosonic modes and half-integer fermionic matter modes, together with even Virasoro and odd supercurrent multipliers. Opposite <fermion> signs at the two endpoints make the doubled <fermion> antiperiodic and remove a matter zero mode. The $b_r$ matter variables are distinct from the $bc$ reparameterization <FP ghosts>. Canonical quantization yields $[\alpha_k^m,\alpha_l^n]=k\eta^{mn}\delta_{k+l,0}$ and $\{b_r^m,b_s^n\}=\eta^{mn}\delta_{r+s,0}$.
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