= Nonrelativistic particle field
{title2=$\mathcal L=i\Psi^\dagger\partial_t\Psi-|\nabla\Psi|^2/(2m)$}
= Schrödinger particle field
{c}
{synonym}
This first-order-in-time field theory has an annihilation-field expansion $\Psi=\int a_{\mathbf p}e^{-i\mathbf p^2t/(2m)+i\mathbf p\cdot\mathbf x}\,d^3p/(2\pi)^3$. Its adjoint creates particles; an <antiparticle> creation term is not required by a relativistic <mass shell> or Lorentz-invariant <microcausality>. It is often an effective low-energy sector of a relativistic charged theory after the <antiparticle> sector is omitted. This does not mean that antimatter cannot be treated nonrelativistically: one may introduce a separate nonrelativistic field for that species.
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