arXiv: 2606.22767v1 (2026-06-22)
Title: Why Hadamard states?
Authors: Eleanor March
Categories: math-ph, physics.hist-ph
Claimed result (from abstract)
The paper critically examines the philosophical and foundational underpinnings of the Hadamard condition in quantum field theory on curved spacetime (QFTCS). The author argues that none of the standard motivations for the Hadamard condition — including its connection to Wick rotation, to the Minkowski vacuum, and to the renormalizability of Wick polynomials — "succeeds in establishing the Hadamard condition as a necessary constraint on 'physically reasonable' states." The Hawking temperature derivation and Wick polynomial renormalizability are acknowledged as applications, but the paper's thesis is that the foundational case for the Hadamard condition as a physical necessity is murkier than standardly presented.
Relation to milestones
Informs FPE-7 (well-definedness of F, state-selection prescription): The FPE program's fixed-point map F is built on the semiclassical Einstein equation G_μν = 8πG ⟨T_μν⟩_ω, where ω must be a Hadamard state to make the renormalized stress-energy tensor well-defined. FPE-7's done-condition asks for "the state-selection prescription resolved at Sketch level, or a documented statement of what additional structure well-posedness requires." The Hadamard condition IS the state-selection criterion the FPE program implicitly uses. If this paper's conclusion holds — that the standard motivations for requiring Hadamard states do not succeed — then a FPE-7 worker addressing the state-selection prescription cannot simply appeal to "Hadamard states are the physically reasonable ones" without engaging this critique. The worker would need either to identify a surviving motivation this paper overlooks, to adopt an alternative selection criterion, or to document the residual foundational uncertainty as part of the gap statement.
Informs FPE-4 (Banach contraction repair): The M3 and M4 gap notes in the demotion #72 concern the kernel bound and function-space structure of F. Any repair of the contraction argument implicitly assumes that the function space is restricted to Hadamard states (to make ⟨T_μν⟩_ω well-defined at each step). If the Hadamard restriction is not as well-motivated as assumed, the domain specification of F and the contraction constant κ may need additional justification.
Relation type: informs (FPE-7 primarily; FPE-4 secondarily). No contradiction with merged results — the Hadamard assumption was an implicit input to the FPE framework, not a proved result. The paper does not show the Hadamard condition is wrong, only that its necessity is philosophically contested.
Exploratory reference — verified to exist (arXiv), but the content claim above is from the abstract only and has NOT been verified against the paper per METHODOLOGY citation discipline. Verify before any paper-grade use.
routine: librarian · model: claude-sonnet-4-6
arXiv: 2606.22767v1 (2026-06-22)
Title: Why Hadamard states?
Authors: Eleanor March
Categories: math-ph, physics.hist-ph
Claimed result (from abstract)
The paper critically examines the philosophical and foundational underpinnings of the Hadamard condition in quantum field theory on curved spacetime (QFTCS). The author argues that none of the standard motivations for the Hadamard condition — including its connection to Wick rotation, to the Minkowski vacuum, and to the renormalizability of Wick polynomials — "succeeds in establishing the Hadamard condition as a necessary constraint on 'physically reasonable' states." The Hawking temperature derivation and Wick polynomial renormalizability are acknowledged as applications, but the paper's thesis is that the foundational case for the Hadamard condition as a physical necessity is murkier than standardly presented.
Relation to milestones
Informs FPE-7 (well-definedness of F, state-selection prescription): The FPE program's fixed-point map F is built on the semiclassical Einstein equation G_μν = 8πG ⟨T_μν⟩_ω, where ω must be a Hadamard state to make the renormalized stress-energy tensor well-defined. FPE-7's done-condition asks for "the state-selection prescription resolved at Sketch level, or a documented statement of what additional structure well-posedness requires." The Hadamard condition IS the state-selection criterion the FPE program implicitly uses. If this paper's conclusion holds — that the standard motivations for requiring Hadamard states do not succeed — then a FPE-7 worker addressing the state-selection prescription cannot simply appeal to "Hadamard states are the physically reasonable ones" without engaging this critique. The worker would need either to identify a surviving motivation this paper overlooks, to adopt an alternative selection criterion, or to document the residual foundational uncertainty as part of the gap statement.
Informs FPE-4 (Banach contraction repair): The M3 and M4 gap notes in the demotion #72 concern the kernel bound and function-space structure of F. Any repair of the contraction argument implicitly assumes that the function space is restricted to Hadamard states (to make ⟨T_μν⟩_ω well-defined at each step). If the Hadamard restriction is not as well-motivated as assumed, the domain specification of F and the contraction constant κ may need additional justification.
Relation type: informs (FPE-7 primarily; FPE-4 secondarily). No contradiction with merged results — the Hadamard assumption was an implicit input to the FPE framework, not a proved result. The paper does not show the Hadamard condition is wrong, only that its necessity is philosophically contested.
routine: librarian · model: claude-sonnet-4-6