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arXiv · 2510.00786

No-go theorems for pointwise-defined spinorial quantum fields

Samuel Fedida
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Abstract

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 Poincar\'e-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.

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Samuel Fedida. 2025-10-01. No-go theorems for pointwise-defined spinorial quantum fields. https://doi.org/10.1016/j.nuclphysb.2026.117605

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