Galilean Reeh--Schlieder Obstruction
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917445461082112 |
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| author | Pachon, Leonardo A. |
| author_facet | Pachon, Leonardo A. |
| contents | We prove that the standard Galilean Haag--Kastler axioms, augmented by Bargmann mass superselection, are inconsistent with the Reeh--Schlieder property: no such net admits a vacuum that is cyclic and separating for every local field algebra. Two ingredients combine: Galilean Schrödinger fields annihilate the Fock vacuum, and Bargmann mass superselection forbids the Hermitian-combination evasion that keeps relativistic axioms consistent. The result extends beyond the Fock-representation hypothesis: any Galilean Haag--Kastler net whose canonical fields carry definite Bargmann mass charges and admit time-zero restrictions on a field-algebra-stable common dense domain is incompatible with Reeh--Schlieder. The bounded-below mass spectrum and the vacuum-at-spectral-minimum, usually imposed as separate axioms, are derived consequences -- of positive-energy boost positivity and a Bose-CCR algebraic descent, respectively. The Tomita--Takesaki modular flow is consequently unavailable on Galilean local field algebras. We identify the Reeh--Schlieder property as the precise structural ingredient distinguishing relativistic from Galilean algebraic quantum field theory: relativistic AQFT has it as a theorem, Galilean AQFT cannot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26271 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Galilean Reeh--Schlieder Obstruction Pachon, Leonardo A. Quantum Physics General Relativity and Quantum Cosmology Mathematical Physics We prove that the standard Galilean Haag--Kastler axioms, augmented by Bargmann mass superselection, are inconsistent with the Reeh--Schlieder property: no such net admits a vacuum that is cyclic and separating for every local field algebra. Two ingredients combine: Galilean Schrödinger fields annihilate the Fock vacuum, and Bargmann mass superselection forbids the Hermitian-combination evasion that keeps relativistic axioms consistent. The result extends beyond the Fock-representation hypothesis: any Galilean Haag--Kastler net whose canonical fields carry definite Bargmann mass charges and admit time-zero restrictions on a field-algebra-stable common dense domain is incompatible with Reeh--Schlieder. The bounded-below mass spectrum and the vacuum-at-spectral-minimum, usually imposed as separate axioms, are derived consequences -- of positive-energy boost positivity and a Bose-CCR algebraic descent, respectively. The Tomita--Takesaki modular flow is consequently unavailable on Galilean local field algebras. We identify the Reeh--Schlieder property as the precise structural ingredient distinguishing relativistic from Galilean algebraic quantum field theory: relativistic AQFT has it as a theorem, Galilean AQFT cannot. |
| title | Galilean Reeh--Schlieder Obstruction |
| topic | Quantum Physics General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2604.26271 |