The Continuum Limit and Integral Vacuum Charge
A Calogeracos, N Dombey
我们研究了一个在连续极限下给出非整数真空电荷的常用公式。我们表明，限制是微妙的，必须采取措施，以获得正确的结果。
We investigate a commonly used formula which seems to give non-integral vacuum charge in the continuum limit. We show that the limit is subtle and care must be taken to get correct results.
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We present a new method for the consistent construction of time-continuous coherent-state path integrals using the theory of half-form quantization. Through the inversion of the quantization procedure we construct a de-quantization map taking first order operators to their corresponding path integrals. We generalize our results using functional techniques, allowing for the consistent path integral study of more general operators, including higher orders and interactions.
The authors of the recent paper [Phys. Rev. A 90, 032104 (2014)] claim to have established a time continuous formulation of path integration in the CS basis free from the mentioned inconsistency. Since a few recent investigations consider the approach advocated in [Phys. Rev. A 90, 032104 (2014)] as providing a "remedy" for the CS path-integral anomaly , I feel it is appropriate to show that the "recipe" proposed does not eliminate the anomaly.
Coherent state path integrals in the continuum
我们讨论了时间连续的路径积分的相干态的基础上的方式是免费的不一致。利用这个概念，我们再现了已知的和精确的结果，直接在连续体中工作。这种形式主义可以为发展量子场论界已知的微扰和非微扰近似奠定基础。这些技术可以被证明是有用的，在各种各样的问题，其中玻色子哈密顿。
The continuum limit of a tensor network: a path integral representation
我们认为，自然的方式来推广张量网络变分类的连续量子系统是使用费曼路径积分实现连续张量收缩。这种方法示出的情况下，最近推出的一类量子场状态被称为连续矩阵产品状态（cMPS）。作为一个例子的效用的路径积分表示，我们认为，一个动态演化的量子场的状态承认一个自然的表示为cMPS。当变分参数的个数趋于无穷大时，Fock空间中的所有状态都可以用cMPS表示.
We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.
Vacuum polarization correction to atomic energy levels in the path integral formalism
本文在全阶处理强核场的路径积分框架中，结合 Dyson-Schwinger 方程推导有效势，计算束缚电子能级至二阶的真空极化修正，并给出数值结果以支持精密质谱检验。
Resolving problems with the continuum limit in coherent-state path integrals
针对玻色子热相干态路径积分中的连续极限问题，通过构造精确离散版本并比较不同排序的连续极限，证明Weyl排序适用于所有多项式哈密顿量，并利用重整化方法给出一般性证明。
Path integral predictions for pre-asymptotic false vacuum decay
针对一般初始态隧穿早期损失大量概率、现有路径积分分析仅捕捉渐近行为的问题，本工作从第一性原理路径积分视角结合steadyon图景的半经典方法研究前渐近区行为，为非微扰隧穿率计算提供可系统改进的框架。
Vacuum charge fractionlization re-examined
我们考虑了一个基于一维Dirac方程的量子化费米子场模型，重新研究了当外加势作用时真空的费米子数或真空电荷的变化情况，利用这个模型，真空电荷的分数化已经在文献中得到了证明，即外加势可以使真空电荷从零变为分数.在这个过程中，电荷守恒似乎被破坏了。这是因为在本文中所考察的电荷只是真空总电荷的一部分。总电荷守恒。除非狄拉克方程有一个零模，否则它不会被分数化。另外两个令人困惑的方面进行了讨论。一个是关于连续极限的使用，另一个是关于当前算子的正则化。这些方面的真空问题的影响进行了探讨。
New Approach to Continuum Path Integrals for Particles and Fields
为了研究欧氏时空中粒子和场的量子涨落，提出了一种近似计算连续Feynman路径积分的方法。路径由高斯函数的和描述，并通过Metropolis方法用exp（-S）加权。加权光滑路径再现了一维谐振子基态的性质，精度在90%以上，并且使用更小的高斯函数宽度可以得到更高的精度。我们的方法应用于量子场论，四维U（1）和SU（2）规范场的量子涨落分别通过威尔逊圈提供了定性水平的库仑力和限制线性势.发现大值规范场的分布至少是指数地受到抑制。
We numerically study the single-flavor Schwinger model with a topological $θ$-term, which is practically inaccessible by standard lattice Monte Carlo simulations due to the sign problem. By using numerical methods based on tensor networks, especially the one-dimensional matrix product states, we explore the non-trivial $θ$-dependence of several lattice and continuum quantities in the Hamiltonian formulation. In particular, we compute the ground-state energy, the electric field, the chiral fermion condensate, and the topological vacuum susceptibility for positive, zero, and even negative fermio…
On the use of complex GTOs for the evaluation of radial integrals involving oscillating functions
该研究针对含束缚态与连续态单电子态乘积的两类径向积分，提出用复GTO展开连续态以实现解析求解的方法，验证了其低能参数下的可靠性，为分子散射应用铺垫基础。
Multicentric integrals that involve a continuum state cannot be evaluated with the usual quantum chemistry tools and require a special treatment. We consider an initial molecular bound state described by multicenter spherical or cartesian Gaussian functions. An electron ejected through an ionization process will be described by an oscillating continuum wavefunction that enters the matrix element necessary for cross section calculations. Within a monocentric approach, we have recently shown how such integrals can be evaluated analytically by using a representation of the continuum state by a se…
The zeta-regularization allows to establish a connection between Feynman's path integral and Fourier integral operator zeta-functions. This fact can be utilized to perform the regularization of the vacuum expectation values in quantum field theories. In this proceeding, we will describe the concept of the zeta-regularization, give a simple example and demonstrate that quantum computing can be employed to numerically evaluate zeta-regulated vacuum expectation values on a quantum computer.
It has recently been shown that vacuum expectation values and Feynman path integrals can be regularized using Fourier integral operator $ζ$-function, yet the physical meaning of these $ζ$-regularized objects was unknown. Here we show that $ζ$-regularized vacuum expectations appear as continuum limits using a certain discretization scheme. Furthermore, we study the rate of convergence for the discretization scheme using the example of a one-dimensional hydrogen atom in $(-π,π)$ which we evaluate classically, using the Rigetti Quantum Virtual Machine, and on the Rigetti 8Q quantum chip "Agave" d…
Extended Electrodynamics: III. Free Photons and (3+1)-Soliton- like Vacuum Solutions
本文的目的是明确地给出我们的非线性场方程的所有非线性真空解，并以坐标自由的方式定义了非线性解的重要子类，我们称之为几乎光子类。通过正确地引入这些解的定域和积分内禀角动量，我们通过要求类光子解的积分内禀角动量等于Planck常数来分离类光子解。最后，我们考虑这样的解决方案，径向移动到或从一个给定的中心，使用标准球坐标。
Non-Markovian dynamics and strong coupling between atomic transitions and a waveguide continuum edge
在量子通信和分布式量子计算中，一维波导提供了量子信息的定向传输。单模波导在较低的截止频率处具有状态密度奇异性，这类似于腔的尖锐谐振，但具有非马尔可夫动力学。因此，我们提出了耦合原子跃迁和波导连续边缘的方案。我们首先提出了一个工作在非马尔可夫区的$Λ$型三能级系统与波导耦合的自旋光子量子界面方案。然后，我们表明，原子跃迁和波导连续边缘之间的强耦合可以导致真空拉比振荡和束缚极化激元状态。
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