Related papers: Pointwise spinor quantum fields cannot be microcausal nor Poincaré covariant

Pointwise spinor quantum fields cannot be microcausal nor Poincaré covariant

URL: http://arxiv.org/abs/2510.00786v1
Date: Wed, 01 Oct 2025 11:32:31 GMT
Title: Pointwise spinor quantum fields cannot be microcausal nor Poincaré covariant
Authors: Samuel Fedida,
Abstract summary: We show that the weak continuity of quantum fields rules out equal-time canonical conjugate (anti)commutation relations in globally hyperbolic spacetimes.<n>We extend Wightman's no-go theorem to show that the weak continuity of quantum fields rules out fermionic microcausality in $C2$ Lorentzian spacetimes.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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 also extend Wightman's no-go theorem to show that the weak continuity of quantum fields rules out fermionic microcausality in $C^2$ Lorentzian spacetimes. We finish by generalising Wizimirski's no-go theorem to show that the existence of a Poincar\'e-invariant vacuum precludes pointwise spinorial covariance on a Minkowski background -- ruling out, in particular, pointwise covariance for Weyl and Dirac fermions, for photons and gravitons -- which further highlights the difficulty of quantising gravity pointwisely.

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