Sectorial Green Functions in the Ternary Algebra C3 and Their Curved-Space Extension
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908544827129856 |
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| author | Aktaş, Bora |
| author_facet | Aktaş, Bora |
| contents | Green functions associated with higher-order differential operators typically lead to special-function expressions in curved or bounded geometries, obscuring analytic transparency. In this work we develop the sectorial Green function for the cubic operator $(D^3+1)$ within the ternary algebra $C_3$ (defined by $j^3=-1$). The algebra admits three exponential carriers and divides the complex plane into six Stokes sectors, in each of which the Green kernel assumes a closed exponential--trigonometric form. We compute explicit responses to box and Gaussian sources, extend the construction to higher algebras $C_4$ and $C_5$, and interpret the resulting kernels as propagators for multi-carrier quantum systems. The central novelty is that, unlike the quadratic $(D^2+1)$ case where curved backgrounds induce Bessel or Airy functions, the $C_3$ Green function in curved space reduces exactly to its flat-space form upon reparametrization by the geodesic coordinate. Curvature merely deforms the coordinate without altering the analytic structure, ensuring closed-form transparency even in curved geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14244 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sectorial Green Functions in the Ternary Algebra C3 and Their Curved-Space Extension Aktaş, Bora General Mathematics Green functions associated with higher-order differential operators typically lead to special-function expressions in curved or bounded geometries, obscuring analytic transparency. In this work we develop the sectorial Green function for the cubic operator $(D^3+1)$ within the ternary algebra $C_3$ (defined by $j^3=-1$). The algebra admits three exponential carriers and divides the complex plane into six Stokes sectors, in each of which the Green kernel assumes a closed exponential--trigonometric form. We compute explicit responses to box and Gaussian sources, extend the construction to higher algebras $C_4$ and $C_5$, and interpret the resulting kernels as propagators for multi-carrier quantum systems. The central novelty is that, unlike the quadratic $(D^2+1)$ case where curved backgrounds induce Bessel or Airy functions, the $C_3$ Green function in curved space reduces exactly to its flat-space form upon reparametrization by the geodesic coordinate. Curvature merely deforms the coordinate without altering the analytic structure, ensuring closed-form transparency even in curved geometries. |
| title | Sectorial Green Functions in the Ternary Algebra C3 and Their Curved-Space Extension |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2509.14244 |