Minimization of an Energy Functional for an Electron in the quantized Radiation Field over quasifree States
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916860674441216 |
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| author | Herdzik, Matthias |
| author_facet | Herdzik, Matthias |
| contents | Building upon the works of Bach, Breteaux, and Tzaneteas (2013) and of Bach and Hach (2022), the Bogolubov-Hartree-Fock (BHF) energy of the Pauli-Fierz Hamiltonian is investigated. Upper and lower bounds on the BHF energy are derived, which suggest positivity of the minimizer, see Theorem IV.6. Under the assumption that the minimizer is indeed positive, a necessary condition on the minimizer is determined by introducing a parameterization, which simplifies the functions of operators appearing in the energy functional. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_17767 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimization of an Energy Functional for an Electron in the quantized Radiation Field over quasifree States Herdzik, Matthias Mathematical Physics 81V10, 81T16 Building upon the works of Bach, Breteaux, and Tzaneteas (2013) and of Bach and Hach (2022), the Bogolubov-Hartree-Fock (BHF) energy of the Pauli-Fierz Hamiltonian is investigated. Upper and lower bounds on the BHF energy are derived, which suggest positivity of the minimizer, see Theorem IV.6. Under the assumption that the minimizer is indeed positive, a necessary condition on the minimizer is determined by introducing a parameterization, which simplifies the functions of operators appearing in the energy functional. |
| title | Minimization of an Energy Functional for an Electron in the quantized Radiation Field over quasifree States |
| topic | Mathematical Physics 81V10, 81T16 |
| url | https://arxiv.org/abs/2507.17767 |