Non-relativistic limit of generalized relativistic Pauli operators by Feynman-Kac formulae
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909021658677248 |
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| author | Sakamoto, Soichiro |
| author_facet | Sakamoto, Soichiro |
| contents | The non-relativistic limit of a generalized relativistic Pauli operator\[H_c^{S,α}=\left(2c^β\bigl(σ\cdot(-i\nabla-a)\bigr)^2+(mc^γ)^{2/α}\right)^{α/2}-mc^γ+V\]on $L^2(\mathbb{R}^3;\mathbb{C}^2)$ is investigated under the constraint$2α=γβ+γ^2$.This operator generalizes the relativistic Pauli operator within the framework of Bernstein functions.The associated heat semigroup $e^{-tH_c^{S,α}}$ admits a Feynman--Kac representation involving Brownian motion, a subordinator, and a Poisson process.Using this representation, we prove that the semigroup $e^{-tH_c^{S,α}}$ converges strongly to $e^{-tH^{S,α}}$ as $c\to\infty$, where the limiting generator is given by\[H^{S,α}=\fracα{2m^{\frac{2}α-1}}\bigl(σ\cdot(-i\nabla-a)\bigr)^2+V.\]The non-relativistic limit of a generalized relativistic Schrödinger operator is also investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06099 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-relativistic limit of generalized relativistic Pauli operators by Feynman-Kac formulae Sakamoto, Soichiro Mathematical Physics The non-relativistic limit of a generalized relativistic Pauli operator\[H_c^{S,α}=\left(2c^β\bigl(σ\cdot(-i\nabla-a)\bigr)^2+(mc^γ)^{2/α}\right)^{α/2}-mc^γ+V\]on $L^2(\mathbb{R}^3;\mathbb{C}^2)$ is investigated under the constraint$2α=γβ+γ^2$.This operator generalizes the relativistic Pauli operator within the framework of Bernstein functions.The associated heat semigroup $e^{-tH_c^{S,α}}$ admits a Feynman--Kac representation involving Brownian motion, a subordinator, and a Poisson process.Using this representation, we prove that the semigroup $e^{-tH_c^{S,α}}$ converges strongly to $e^{-tH^{S,α}}$ as $c\to\infty$, where the limiting generator is given by\[H^{S,α}=\fracα{2m^{\frac{2}α-1}}\bigl(σ\cdot(-i\nabla-a)\bigr)^2+V.\]The non-relativistic limit of a generalized relativistic Schrödinger operator is also investigated. |
| title | Non-relativistic limit of generalized relativistic Pauli operators by Feynman-Kac formulae |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2605.06099 |