Positivity and Microcausality in Scalar–Vector–Spinor Effective Field Theory

A five-dimensional scalar–vector–spinor effective field theory (SVS-EFT) requires a physical state space and a causal kinetic operator in addition to its Clifford-algebraic organization. We construct a one-time compact benchmark that makes these requirements explicit and separates them from a proposed projection in the real algebra . The proposed map fails idempotency, whereas the spacelike compact operator with a unitary twist yields a positive, stable four-dimensional spectrum. For two probes separated by half the circumference, we derive an exact normalized transfer identity that factorizes the holonomy and geometric attenuation. Antiperiodicity cancels the entire cross-response without removing local physical states. We prove that a nonzero finite sum of ordinary particle poles cannot reproduce the exact interval before compact first arrival, although each retained mode remains four-dimensionally microcausal. A symmetry-preserving cutoff protects the interference zero; an unpaired cutoff produces a calculable false signal. We also specify the representation-dependent relation between the compact twist and a metaplectic angle, and verify the leading scalar absorptive cut. An exact scattering-space leakage identity states the additional condition required for a projected sector to close. These results give the SVS-EFT programme a concrete consistency benchmark without assuming an interacting completion.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-06
DOI
https://doi.org/10.5281/zenodo.24012107
Primary Topic
Relativity and Gravitational Theory
Type
article
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article

Positivity and Microcausality in Scalar–Vector–Spinor Effective Field Theory

Ying Ye
4 links
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
article

Positivity and Microcausality in Scalar–Vector–Spinor Effective Field Theory

Ying Ye
article en

Abstract

A five-dimensional scalar–vector–spinor effective field theory (SVS-EFT) requires a physical state space and a causal kinetic operator in addition to its Clifford-algebraic organization. We construct a one-time compact benchmark that makes these requirements explicit and separates them from a proposed projection in the real algebra . The proposed map fails idempotency, whereas the spacelike compact operator with a unitary twist yields a positive, stable four-dimensional spectrum. For two probes separated by half the circumference, we derive an exact normalized transfer identity that factorizes the holonomy and geometric attenuation. Antiperiodicity cancels the entire cross-response without removing local physical states. We prove that a nonzero finite sum of ordinary particle poles cannot reproduce the exact interval before compact first arrival, although each retained mode remains four-dimensionally microcausal. A symmetry-preserving cutoff protects the interference zero; an unpaired cutoff produces a calculable false signal. We also specify the representation-dependent relation between the compact twist and a metaplectic angle, and verify the leading scalar absorptive cut. An exact scattering-space leakage identity states the additional condition required for a projected sector to close. These results give the SVS-EFT programme a concrete consistency benchmark without assuming an interacting completion.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 26%
Relativity and Gravitational Theory
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