Antiperiodic boundary condition (source code)

= Antiperiodic boundary condition
{title2=$f(x+L)=-f(x)$}

An <antiperiodic boundary condition> is a phase twist of $\pi$ across the boundary. A Fourier mode then has $k=2\pi(n+1/2)/L$. It occurs in the even-fermion sector of a periodic <Jordan–Wigner transformation> and in imaginary-time fermionic thermal fields, for different underlying reasons.