No-go theorems for pointwise-defined spinorial quantum fields

We extend and strengthen no-go results on pointwise-defined quantum fields to cover general spinors.

We show that the weak continuity of quantum fields rules out equal-time canonical conjugate (anti)commutation relations in globally hyperbolic spacetimes; for quantum fields on Minkowski spacetime, weakly continuous translation covariance enforces the needed continuity and yields the same no-go.

We then prove a fermionic microcausality no-go result: a weakly continuous pointwise fermionic field satisfying local spacelike anticommutation with its adjoint field on a $C^2$ Lorentzian spacetime must vanish.

We finish by generalising Wizimirski's no-go theorem to show that the existence of a Poincaré-invariant separating vacuum precludes pointwise spinorial covariance on a Minkowski background.

The result applies to Weyl and Dirac multiplets and to gauge-invariant field-strength multiplets such as the electromagnetic field strength and the linearised Weyl curvature.

Gauge potentials are covered only when exact tensor covariance, rather than covariance modulo gauge transformations, is imposed.