Pointwise spinor quantum fields cannot be microcausal nor Poincaré covariant
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915528322318336 |
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| author | Fedida, Samuel |
| author_facet | Fedida, Samuel |
| contents | 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 Poincaré-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00786 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pointwise spinor quantum fields cannot be microcausal nor Poincaré covariant Fedida, Samuel General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Quantum Physics 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 Poincaré-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. |
| title | Pointwise spinor quantum fields cannot be microcausal nor Poincaré covariant |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2510.00786 |