Enter, I-B-VP-8-Ex1-v2, 2026, pp. 1-44
I-B-VP-8-Ex Regular Friedrichs thermal one-point functions Wick square, stress tensor, and charged current before any apex extension
Ngo Cheung
2026
Abstract
For the prescribed four-dimensional ultrastatic cone, an arbitrary fixed flat character, and the massless Friedrichs realization, we construct the regular-host Wick square, stress tensor, and charged current of the centered zero-chemical-potential Bose KMS state at every inverse temperature B_T > 0. The principal contribution is the missing compact-test-to-coincidence bridge: weak Euclidean periodization is upgraded to normally convergent differentiated image sums near every regular diagonal point, after an independent check of the local Hadamard subtraction. The current is calculated from the imaginary angular first jet, not inferred from its vacuum value.
The resulting formulas give an explicit positive zeta-function coefficient for the leading thermal Wick correction,
δF(r) ∼ (d_{*}ζ(2 + 2ν_{*}))/(2π²α B_T^{2 + 2ν_{*}}) r^{2ν_{*}},
including the untwisted value δF(0 +) = 1/(12αB_T²). They also give the corresponding signed lowest-mode coefficient of the thermal current, a strictly nonzero longitudinal boost-breaking stress difference at every positive temperature, and convergence of all three regular one-points to their vacuum values in the fixed-operator zero-temperature limit. These estimates provide a controlled local starting point for subsequent observable calculations without presupposing an apex renormalization.
The contribution is a domain-explicit regular-host package, not a claim that thermal cone Green functions, Bose KMS methods, or vacuum-polarization phenomena are new. A separate finite-register argument explains why a supplied report of these coefficients is neither continuum thermometry nor quantum recovery, and why a heat kernel is not reservoir heat. No apex-contact classification, global thermal wavefront theorem, massive or non-product state construction, backreaction, spacetime-emergence theorem, or inherited gravitational quantum-coefficient admission is asserted.
Bibliographic record
- Title
- I-B-VP-8-Ex Regular Friedrichs thermal one-point functions Wick square, stress tensor, and charged current before any apex extension
- Author
- Cheung, Ngo
- Publication date
- 2026
- Institution
- Enter
- Report number
- I-B-VP-8-Ex1-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 44
- Language
- en