Local quantum fields are operator valued distributions which create and annihilate particles. The fields intertwine the unitary transformations of quantum particles with the adjoint transformations of test functions. The construction of massive fields does not extend continuously to massless fields. For nonvanishing helicity massless fields exist in Hilbert space only if particles come in pairs of opposite helicity and charge. The fields are derivatives of a field which Lorentz transforms as a symmetric power of the fundamental spinor representation or of its conjugate. Other fields, in particular massless vector fields, occur only in a Fock space which also contains negative norm states.