Enter, I-B-VP-3-v2, 2026, pp. 1-44
I-B-VP-3: Massive ground states, vacuum polarization, and the bound-channel threshold
Ngo Cheung
October 2026
Abstract
We construct massive scalar spectral ground states and their renormalized Wick square, mixed stress tensor, and charged azimuthal current on the regular conical product prescribed in I-B. The construction covers every positive-mass regime of the rotation-invariant, longitudinally local product-extension class defined in this paper, including non-Friedrichs extensions with negative transverse bound states.
The decisive distinction is between spectral nonnegativity and infrared admissibility. If −κ_{*}² is the lowest transverse energy, the ordinary compact-test spectral covariance exists for m > κ_{*}. At m = κ_{*} > 0, it fails precisely on tests with a nonzero zero-frequency projection onto a critical bound channel. We identify the finite-codimension restricted test space on which the threshold covariance remains meaningful and prove the universal approach-to-threshold law
H_{W, m} = (log (μ/√(m² − κ_{*}²)))/(2π) Π_{*} + O_{C^{∞}}(1)
near every regular diagonal point. Here Π_{*} is the critical transverse projector kernel and μ > 0 is a reference scale. The resulting observable divergence is a regular-region, extension-dependent infrared effect, not an apex contact or a local ultraviolet counterterm.
For the Friedrichs family, convergent proper-time formulas evaluate all three observables for every cone angle. For the remaining extensions, explicit Bessel resolvent coefficients reduce their observable corrections to absolutely convergent one-dimensional integrals. The complex first jet fixes the massive current, and finite-character quotient formulas independently check its sign and normalization. Conservation, the massive trace identity, curvature-coupling improvement, and compact-regular massless limits are proved.
The contribution is this simultaneous extension-resolved state-and-observable package and its exact threshold diagnosis, not a priority claim for massive cosmic-string polarization. A mass can stabilize a negative transverse channel, but critical nonnegativity does not produce an unrestricted vacuum. The cone, extension, state prescription, and normalization remain inputs. No apex quantum algebra, backreaction, interacting product, continuum acquisition by Enter readout, or Einstein dynamics is constructed.
Bibliographic record
- Title
- I-B-VP-3: Massive ground states, vacuum polarization, and the bound-channel threshold
- Author
- Cheung, Ngo
- Publication date
- 2026/10/01
- Institution
- Enter
- Report number
- I-B-VP-3-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 44
- Language
- en