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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.03944 |
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| _version_ | 1866917256474132480 |
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| author | Barvinsky, Andrei O. Kalugin, Alexey E. Wachowski, Władysław |
| author_facet | Barvinsky, Andrei O. Kalugin, Alexey E. Wachowski, Władysław |
| contents | We consider integral kernels for functions $f(\hat F)$ of a minimal second-order differential operator $\hat F(\nabla)$ on a curved spacetime. We show that they can be expanded in a functional series, analogous to the DeWitt expansion for the heat kernel, by integrating the latter term-by-term. This procedure leads to a separation of two types of data: all information about the bundle geometry and the operator $\hat F(\nabla)$ is still contained in the standard HaMiDeW coefficients $\hat a_k[F | x,x']$ (we call this property ``off-diagonal functoriality''), while information about the function $f$ is encoded in some new scalar functions $\mathbb{B}_α[f | σ]$ and $\mathbb{W}_α[f | σ, m^2]$, which we call basis and complete massive kernels, respectively. These objects are calculated for operator functions of the form $\exp(-τ\hat F^ν)/(\hat F^μ+ λ)$ as multiple Mellin--Barnes integrals. The article also discusses subtle issues such as the validity of the term-by-term integration, the regularization of IR divergent integrals, and the physical interpretation of the resulting expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functorial properties of Schwinger-DeWitt expansion and Mellin-Barnes representation Barvinsky, Andrei O. Kalugin, Alexey E. Wachowski, Władysław High Energy Physics - Theory We consider integral kernels for functions $f(\hat F)$ of a minimal second-order differential operator $\hat F(\nabla)$ on a curved spacetime. We show that they can be expanded in a functional series, analogous to the DeWitt expansion for the heat kernel, by integrating the latter term-by-term. This procedure leads to a separation of two types of data: all information about the bundle geometry and the operator $\hat F(\nabla)$ is still contained in the standard HaMiDeW coefficients $\hat a_k[F | x,x']$ (we call this property ``off-diagonal functoriality''), while information about the function $f$ is encoded in some new scalar functions $\mathbb{B}_α[f | σ]$ and $\mathbb{W}_α[f | σ, m^2]$, which we call basis and complete massive kernels, respectively. These objects are calculated for operator functions of the form $\exp(-τ\hat F^ν)/(\hat F^μ+ λ)$ as multiple Mellin--Barnes integrals. The article also discusses subtle issues such as the validity of the term-by-term integration, the regularization of IR divergent integrals, and the physical interpretation of the resulting expansions. |
| title | Functorial properties of Schwinger-DeWitt expansion and Mellin-Barnes representation |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.03944 |