= Quantum field
{title2=$\Phi(x)$}
A <quantum field> is an operator-valued <distribution> on spacetime: smearing $\Phi(x)$ against a smooth test function gives an operator, whereas pointwise products can require renormalization. For example, a free <complex scalar field> contains particle <annihilation operators> and <antiparticle> <creation operators>. Its <microcausality> condition makes field commutators vanish at spacelike separation. For <fermions>, the corresponding locality condition uses anticommutators. This combines quantum operators with the spacetime locality of a <quantum field theory>.
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