Toshimitsu Takaesu
In this paper the Hamiltonian of quantum electrodynamics with spatial cutoffs is investigated. We define a scaled total Hamiltonian and consider its asymptotic behavior. In the main theorem, it is shown that the scaled total Hamiltonian converges to a self-adjoint operator in the strong resolvent sense, and effective potentials are derived.
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On the Spectral Analysis of Quantum Electrodynamics with Spatial Cutoffs. I
本文研究了具有空间截止的量子电动力学模型的谱。证明了：（1）该哈密顿量是自伴的;（2）在红外正则性条件下，当耦合常数足够小时，该哈密顿量存在唯一的基态.研究了光谱散射理论，证明了渐近场的存在和光谱间隙的闭合。
In this paper, we investigate a system of quantum electrodynamics with cutoffs. The total Hamiltonian is defined on a tensor product of a fermion Fock space and a boson Fock. It is shown that, under spatially localized conditions and momentumregularity conditions, the total Hamiltonian has a ground state for all values of coupling constants. In particular, its multiplicity is finite.
Quantum electrodynamics of relativistic bound states with cutoffs
本文考虑一个具有紫外和红外截止的哈密顿量，描述库仑势中的相对论电子和正电子与库仑规范中光子的相互作用。这种相互作用包括电流密度与横向光子的相互作用和电荷密度与自身的库仑相互作用。我们证明了当耦合常数足够小时，该哈密顿量是自伴的，并且具有基态。
Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics
我们证明了当N <Z+1时，描述N个自旋非相对论电子与量子化辐射场和几个总电荷为Z的固定核相互作用的哈密顿量存在一个基态。结果适用于任何值的精细结构常数α和任何值的紫外截止λ的辐射场。没有红外线截止。在我们的证明中，基本的数学成分是一种新的定位电磁场的方法，以这种方式，能量的误差小于1/L，其中L是定位半径。
We show that relativistic quantum electrodynamics in the Coulomb gauge satisfies the following bound, which establishes stability: let $H(Λ,V)$ denote the Hamiltonian of $QED_{1+3}$ on the three-dimensional torus of volume $V$ and with ultraviolet cutoff $Λ$. Then there exists a constant $0<μ(Λ,V)<\infty$ (the vacuum energy renormalization) such that the renormalized Hamiltonian is positive: $H_{ren}(Λ,V) \equiv H_{Λ,V}+μ_{Λ, V}\cdot \mathbb{1} \ge 0 $.
Ground States in Non-relativistic Quantum Electrodynamics
与量子化电磁场和外部电势相互作用的带电粒子的激发态都会衰减，但这样的粒子应该有一个真正的基态--一个能量最小并满足薛定谔方程的基态。我们相当普遍地证明，这种状态存在的{ \it所有值}的精细结构常数和紫外截止。我们也证明了在自然物理条件下多粒子系统的同样情况。
Quasi-static Limits in Nonrelativistic Quantum Electrodynamics
考虑N个自旋为1/2的非相对论性粒子与量子化麦克斯韦场（质量为零，自旋为1）的相互作用系统，当粒子的速度很小时，系统的相互作用受到紫外截止，但没有红外截止.两种方法来实现的限制被认为是：C去无穷大的粒子的速度v固定，严格的结果已经在文献中讨论的情况下，和v去0与C固定。第二种情况可以重新表述为重粒子的极限，m_{j}-->^{-2} m_{j}，在长时间内观察到，t-->^{-1} t，--> 0 ^{+}，动能E_{kin} = Or（1）。专注于第二种方法，我们构造的子空间是不变的动力学项的顺序<$sqrt {log（<$^{-1}）}和描述有效的动力学，只为粒子，在他们里面。在最低阶，粒子通过库仑势相互作用。在第二个条件下，质量得到了电磁场的修正，并出现了速度相关的相互作用，即达尔文项。此外，我们还计算了波函数的辐射段，即波函数的辐射段.例如，从几乎不变子空间中泄漏出来的部分，并计算相应的辐射能量。
A direct derivation of an effective Hamiltonian in non-relativistic quantum electrodynamics
本文通过不依赖缩放极限的方法，直接推导出非相对论量子电动力学中的Arai有效哈密顿量，适用于更广泛的势场类别，包括Rollnik类和约束势如谐振子势。
Mass and Spin Renormalization in Lorentz Electrodynamics
提出了一种新的相对论协变的有质量洛伦兹电动力学（LED），其中裸粒子具有有限的正裸静止质量和转动惯量.粒子的电磁自相互作用使其质量和自旋重新正规化。最重要的是，重整化粒子是一个孤立子：在任何散射过程之后，它的静止质量和自旋幅度动态地恢复到它们散射前的值。这保证了“电子仍然是电子”，诗意地说。对这个模型进行了重整化流研究，讨论了裸静止质量消失的极限。这个极限产生了一个纯电磁经典场论，其紫外截止波长大约是电子的康普顿波长！重整化极限模型与经验电子数据相匹配，就像人们在洛伦兹理论水平上所希望的那样有序。特别是，没有超光速赤道回转速度发生。
Mass Renormalization in Non-relativistic Quantum Electrodynamics with Spin 1/2
研究了具有紫外截止的Pauli-Fierz哈密顿量的有效质量$\mass$和自旋为1/2的非相对论QED中的裸质量$m$.给出了$\mass$在耦合常数$e$中的解析性质，并给出了依赖于$Λ/m$的常数$a_1(Λ/m)$和$a_2(Λ/m)$的显式形式，使得$$\mass/m =1 + a_1(Λ/m) e^2+ a_2(Λ/m) e^4+ {\mathcal O}(e^6)$$.结果表明，自旋相互作用增强了有效质量，并且存在严格的正常数$b_1,b_2, c_1$和$c_2$，使得$$\d b_1\leq \lim_{Λ\to\infty} \frac{a_1(\Lamdda/m)}{\log (Λ/m)}\leq b_2, c_1\leq \lim_{Λ\to\infty} \frac{a_2(Λ/m)}{(Λ/m)^2}\leq -c_2.$$特别是$a_2(Λ/m)$不发散为$\pm [\log(Λ/m)]^2$，而是发散为$-(Λ/m)^2$ .
A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics
我们研究了三种著名的物质模型，它们分别与紫外截止、量子化辐射场和任意多个原子核的库仑势耦合。其中两个是非相对论性的：第一个使用动能（p+eA（x））^2，第二个使用保利-菲尔斯能量（p+eA（x））^2 +eσ \cdot B（x）。第三种是非对模型，它是相对论性的，用狄拉克算子D（A）代替了动能，但仅限于它的正谱子空间，即“电子子空间”。在每种情况下，我们都能给出{ \it结合}能的上限--与较不困难的基态能不同。这意味着，我们第一次相信，对这些理论中的质量重整化的估计，尽管是粗略的。
Hamiltonian models based on two different infrared approximations are studied in order to obtain an explicit comparison with the standard analysis of the infrared contributions, occurring in the relativistically covariant perturbative formulation of Quantum Electrodynamics. Moller operators, preserving respectively the Hilbert scalar product, for the Coulomb-gauge models, and an indefinite metric, for the models formulated in Feynman's gauge, are obtained in the presence of an infrared cutoff, after the removal of an adiabatic switching and with the aid of a suitable mass renormalization. In t…
Stability of a Model of Relativistic Quantum Electrodynamics
量子电动力学的相对论性“非对”模型使用狄拉克算符D（A）以及库仑规范中量子化紫外截止电磁场A的通常自能来描述电子动力学。没有正电子，因为电子的波函数被限制在某个狄拉克算符D的正谱子空间中，但该模型被定义为任意数量N的电子，因此描述了一个真正的多体系统。除了电子之外，还有K个带电荷\leq Z的固定原子核。如果场不是量子化的，而是经典的，那么前面已经表明，如果使用习惯的D（0）来定义电子空间，那么这样的模型总是不稳定的（基态能量E=- \infty），但是是稳定的（E > -const）。（N+K）），如果使用D（A）本身（假设精细结构常数α和Z不是太大）。本文将这一结果推广到量子化场，并证明了α=1/137和Z \leq 42时的稳定性. QED的这种表述有些不寻常，因为它意味着电子希尔伯特空间与光子福克空间密不可分。但这种联系似乎更好地描述了光子和电子的真实世界。
We derive upper and lower bounds on the convergence behavior of certain classes of one-parameter quantum dynamical semigroups. The classes we consider consist of tensor product channels and of channels with commuting Liouvillians. We introduce the notion of Cutoff Phenomenon in the setting of quantum information theory, and show how it exemplifies the fact that the convergence of (quantum) stochastic processes is not solely governed by the spectral gap of the transition map. We apply the new methods to show that graph states can be prepared efficiently, albeit not in constant time, by dissipat…
Group field theory is a generalization of matrix models, with triangulated pseudomanifolds as Feynman diagrams and state sum invariants as Feynman amplitudes. In this paper, we consider Boulatov's three-dimensional model and its Freidel-Louapre positive regularization (hereafter the BFL model) with a ?ultraviolet' cutoff, and study rigorously their scaling behavior in the large cutoff limit. We prove an optimal bound on large order Feynman amplitudes, which shows that the BFL model is perturbatively more divergent than the former. We then upgrade this result to the constructive level, using, i…
A new understanding of grazing limit
该研究针对Boltzmann方程到Landau方程的掠射极限问题，通过对无角截断Boltzmann算子施加自然标度，结合新的适定性理论，在γ>-5的更广参数范围（含库仑势）下论证了极限过程，并揭示了算子的分解特性。
We study two Hamiltonian models, based on infrared approximations which render them solvable, in order to obtain an operator formulation of the soft-photon corrections to the scattering of a single electron, as given in Quantum Electrodynamics by the method of Feynman's diagrams. The first model is based on the same approximations of the Pauli-Fierz Hamiltonian, the second one stems from an expansion in powers of the four-momentum transfer, along the lines of Bloch and Nordsieck. For both models, the dynamics of the charge is accounted for by suitably chosen classical currents, interacting wit…
We show how quantum fields can be used to measure the curvature of spacetime. In particular, we find that knowledge of the imprint that spacetime curvature leaves in the correlators of quantum fields suffices, in principle, to reconstruct the metric. We then consider the possibility that the quantum fields obey a natural ultraviolet cutoff, for example, at the Planck scale. We investigate how such a cutoff limits the spatial resolution with which curvature can be deduced from the properties of quantum fields. We find that the metric deduced from the quantum correlator exhibits a peculiar scali…
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