Enter, I-B-VP-8-v2, 2026, pp. 1-38
I-B-VP-8 Friedrichs thermal states on the prescribed conical spacetime
Ngo Cheung
Version 1
Abstract
We construct the massless, zero-chemical-potential Friedrichs thermal state on the prescribed regular conical product of I-B, for every opening parameter 0 < α < 1, every flat-bundle character 0 ≤ β < 1, and every inverse temperature β_T > 0. The extension, temperature, and Bose prescription remain inputs. The construction precedes, and does not repeat, the thermal one-point extension calculation of I-B-VP-1.
The key analytical distinction is infrared: compact-test ground-state finiteness involves B_F^{−1/4}, whereas positive-temperature field variance requires B_F^{−1/2}. We prove the latter estimate directly. More precisely, if ρ = min_{n ∈ ℤ} |n + β|/α, the compactly tested Friedrichs heat semigroup decays as s^{−3/2 − ρ}. Its leading coefficient is an explicit positive sum of squared lowest-angular-mode moments. This gives an optimal fractional inverse-power threshold for tests with a nonzero leading moment, and a quantitative thermal infrared-tail bound of order ε^{1/2 + ρ}.
We construct a positive, regular, centered quasifree state, prove the full bounded-observable KMS strip condition, verify the extension-selected field equation and commutator, and prove continuity and finite second moments for all compact smooth regular spacetime tests. A weak Euclidean periodization identity identifies its prescribed two-point function without taking coincidence limits. At fixed massless operator, the states converge weakly to the spectral ground state as Tdownarrow 0, with an explicit covariance estimate.
The contribution is a domain-explicit completion of the Friedrichs thermal-state gate and its stronger infrared obligation; thermal cosmic-string Green functions and quasifree KMS methods are established subjects. The inherited no-go for unstable product extensions is retained with its compact-test proof. No massive thermal state, non-Friedrichs or non-product thermal state, excited-state classification, thermal wavefront theorem, new apex-contact classification, or backreaction is constructed.
Bibliographic record
- Title
- I-B-VP-8 Friedrichs thermal states on the prescribed conical spacetime
- Author
- Cheung, Ngo
- Publication date
- 2026
- Institution
- Enter
- Report number
- I-B-VP-8-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 38
- Language
- en