荒牧数学談話会 / 第7回案内
第7回荒牧数学談話会の開催について
群馬大学荒牧キャンパスの教室での対面開催です。
講演内容は以下の通りです。
開催日時・内容
日時：2026年6月4日（木）16:00開始
場所: 群馬大学共同教育学部（荒牧キャンパス） 6号館1階 C104
- 松澤泰道 (信州大学教育学部)
- A direct derivation of an effective Hamiltonian in non-relativistic quantum electrodynamics
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Non-relativistic quantum electrodynamics provides a framework for describing the interaction between charged particles and the quantized electromagnetic field, and plays a fundamental role in understanding the Lamb shift in hydrogen atoms.
Welton explained the Lamb shift based on the physical intuition that vacuum fluctuations of the electromagnetic field induce fluctuations in the position of the electron, which leads to an effective averaging of the potential. This picture can be formulated in terms of an effective Hamiltonian in which the electron potential is modified to incorporate the contribution of the electromagnetic field. Arai derived such an effective Hamiltonian via the scaling limit and studied its spectral properties to derive the Lamb shift.
In this talk, we give a direct derivation of the effective Hamiltonian obtained by Arai, without relying on the scaling limit. We characterize the effective Hamiltonian through expectation values of the total Hamiltonian with respect to dressed electron states. Our approach, based on the theory of quadratic forms, allows us to treat a broader class of potentials, including the Rollnik class and confining potentials such as the harmonic potential.