Enter, I-B-VP-7-v2, 2026, pp. 1-37
I-B-VP-7 Spin structures and first-order Dirac domains on the prescribed conical spacetime
Ngo Cheung
Version 1
Abstract
We address the spin-structure and first-order operator stages of I-B-VP's open spinor and constrained-field row on its unchanged, prescribed regular conical product. The regular host has exactly two spin structures. Their polar-frame signs are independent of the prescribed flat line-bundle character, although the charged spinor equation sees their combined monodromy. We derive the spin connection and the radial Dirac expression explicitly.
For a two-component transverse spinor, the deficient channels are exactly those satisfying
|n + s + β| < α/2, s ∈ {0, 1/2}.
There is at most one such channel. We prove the endpoint criterion, including equality cases, construct its boundary traces, and state all self-adjoint radial domains. Two coordinate-axis domains preserve the transverse grading. Either gives a longitudinal product realization of the massless four-component Hamiltonian, with its full operator domain and an exact graph-norm identity. The unrestricted spatial minimal operator has infinite deficiency indices when a critical channel is present; the finite boundary condition belongs to the chosen transverse product construction.
The principal debugging result is a square-domain obstruction: in a critical channel, no self-adjoint realization of the first-order radial Dirac expression has the componentwise Friedrichs realization of its formal square as its operator square. Thus independently choosing regular scalar squares does not define a Dirac domain. Explicit examples also show that scalar essential self-adjointness does not determine the spinor verdict.
The potential usefulness is a domain-complete interface for later spinor analysis, separating topology, flux, first-order boundary data, and one-point contacts. The underlying spin and Aharonov–Bohm extension theory is established; no general priority claim is made. No vacuum state, current or stress expectation value, quantum Maxwell system, Proca field, twisted tensor sector, backreaction, or inherited characteristic quantum coefficient is constructed.
Bibliographic record
- Title
- I-B-VP-7 Spin structures and first-order Dirac domains on the prescribed conical spacetime
- Author
- Cheung, Ngo
- Publication date
- 2026
- Institution
- Enter
- Report number
- I-B-VP-7-v2
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 37
- Language
- en