大质量光子的限制效应

Massive dual gauge field and confinement in Minkowski space : Electric charge

SU(2) gauge theory in the nonlinear gauge of the Curci-Ferrari type is studied in low-energy region. We give a classical solution that connects color electric charges. Its dual solution, which has a configuration of monopole, is also presented. Due to the gluon condensation subsequent to the ghost condensation, these classical fields become massive. The massive Lagrangian with the classical solution and that with the dual solution are derived. We show that these Lagrangians produce a linear potential between a quark and an antiquark. This is the mechanism of quark confinement that is different…

Condensates, massive gauge fields and confinement in the SU(3) gauge theory

SU(3) gauge theory in the nonlinear gauge of the Curci--Ferrari type is studied. In the low-energy region, ghost condensation and subsequent gauge field condensation can happen. The latter condensation makes classical gauge fields massive. If the color electric potential with string is chosen as the classical gauge field, it produces the static potential with the linear potential. We apply this static potential to the three-quark system, and show, different from the $Y$-type potential, infrared divergence remains in the $Δ$-type potential. The color electric flux is also studied, and show that…

大质量光子与狄拉克单极：电凝聚与磁约束

Massive photons and Dirac monopoles: electric condensate and magnetic confinement

我们使用广义朱莉娅-图卢兹方法（GJTA）的拓扑电流（电荷或缺陷）的凝聚，认为大质量的光子可以共存一致的狄拉克单极。Proca理论是通过GJTA得到的，作为描述电凝聚的低能有效理论，矢量玻色子的质量负责产生迈斯纳效应，该效应将磁缺陷限制在由狄拉克膜不变量而不是狄拉克弦描述的物理开放磁涡旋连接的磁-反磁对中。

具有大量N味费米子的二维QED中的禁闭和手征凝聚

Confinement and chiral condensates in 2-d QED with massive N-flavor fermions

我们计算了零温和有限温下二维量子电动力学中的Polyakov环和弦张力，其中包括无质量和有质量的$N$味费米子。外部电荷或外部电场会在费米子质量中产生相位，并使真空角参数$θ$的值发生变化，这反过来又会改变手征凝聚体。特别地，在存在两个相反电荷源$q$和$-q$的情况下，$θ$的位移是$2π(q/e)$，与$N$无关。对于$N\ge 2$，弦张力在$θ=\pmπ$处具有尖点奇点，并且在$T=0$处与$m^{2N/(N+1)}$成比例。

拓扑大质量$U{\left( 1 \right)_{\cal W}} \times U{(1)_{\cal Y}}$ Chern-Simons-Higgs理论中的屏蔽和禁闭问题

Aspects of screening and confinement in a topologically massive $U{\left( 1 \right)_{\cal W}} \times U{(1)_{\cal Y}}$ Chern-Simons-Higgs theory

通过使用规范不变但依赖于路径的变量形式主义，我们考虑了最近提出的拓扑质量$U{\left( 1 \right)_{\cal W}} \times U{(1)_{\cal Y}}$ Chern-Simons-Higgs理论在$2+1$维。特别地，我们考察了两个阿贝尔规范场之间的陈-西蒙斯混合项对物理观测量的影响。我们通过分析两种不同情况下的模型来进行调查。在第一种情况下，我们整合了大量的激发，并考虑一个有效的模型，为无质量的领域，我们表明，相互作用能包含一个线性项导致的限制的静电荷探针随着屏蔽的贡献。第二种情况下，无质量场可以被精确地积分，并适当地考虑到其约束，有趣的是，由此产生的有效模型描述了一个纯粹的屏蔽相，没有任何限制制度的痕迹。

从禁闭观点看无Higgs场的大质量Yang-Mills理论的物理么正性

Physical unitarity of a massive Yang-Mills theory without the Higgs field from a viewpoint of confinement

在这次演讲中，我们将研究没有希格斯场的大质量杨-米尔斯理论中的物理幺正性，其中色规范对称性不会自发破缺并保持完整。为此，我们使用一个新的框架提出的作者之一的基础上的非阿贝尔场的非微扰建设描述一个大规模的自旋1矢量玻色子场，这使我们能够进行微扰和非微扰研究的物理么正性。此外，在给出了有质量杨-米尔斯理论的一般性质之后，我们提出了一种新的物理么正性微扰处理方法。然后，我们以透明的方式再现对物理幺正性的破坏。这项工作是一个初步的工作，在随后的工作中，我们提出了一个非微扰的框架，提出了一个可能的情况下恢复的Curci-Ferrari模型中的物理幺正性。讨论了色禁闭、胶球质量和BRST不变的二维凝聚对低能QCD的影响。

超场形式中的颜色禁闭与大质量胶子

Color Confinement and Massive Gluon in Superfield Formalism

本文在超场形式中重新审视量子色动力学中的颜色禁闭，证明当胶子场的BRST变换存在束缚态时，胶子获得质量并被禁闭，且其渐近场满足大质量偶极场方程，同时夸克场在禁闭相满足大质量旋量偶极方程，暗示夸克-反夸克对形成束缚态并禁闭为介子，这为解决二次引力中鬼场禁闭及幺正性问题提供了启示。

二次引力中巨影子的禁闭

Confinement of Massive Ghost in Quadratic Gravity

利用协变正则形式，通过BRST四重态机制证明巨影子与Faddeev-Popov影子形成束缚态后被禁闭在零模态中，从而恢复幺正性。

Seiberg-Witten模型中的质量、约束和CP不变性”

Mass, Confinement and CP Invariance in the Seiberg-Witten Model"

本文讨论了具有SU（2）规范群的N=2超对称Yang-Mills理论的Seiberg-Witten解的几个物理问题，并对“物质”场补充了一个小质量项，从而得到了一个具有禁闭的$N=1$理论。在现有代数关系的基础上理解了该理论的光谱，并研究了无质量和有质量理论的CP不变性。我们发现，在有质量（约束）理论中，低能物理具有精确的CP对称性，而在无质量理论中，在一般真空中CP不稳定性是自发破缺的。

光子在拓扑物质中的命运：超导、禁闭和涡旋量子霍尔效应

The Fate of the Photon in Topological Matter: Superconductivity, Confinement and the Vortex Quantum Hall Effect

拓扑物质的特征是在其长距离有效作用中存在拓扑BF项。由于U（1）规范场的紧性而引起的拓扑缺陷导致了拓扑绝缘体、拓扑超导体和拓扑禁闭之间的量子相变。在传统超导中，由于自发对称性破缺，光子由于安德森-希格斯机制而获得质量。本文导出了拓扑超导体和拓扑禁闭相中电磁场的相应有效作用量。在拓扑超导体中，磁通量被限制，光子通过BF机制获得拓扑质量：不涉及对称性破缺，基态具有拓扑秩序，跃迁由量子涨落引起。相反，在拓扑限制中，电荷被线性限制，光子通过施托克堡机制变成一个大质量的反对称张量。当弦凝聚体同时携带磁通量和电通量（双子弦）时，就会出现斜约束相。这种相位的特征在于涡旋量子霍尔效应，其与存储在涡旋上的信息的无耗散传输潜在相关。

有关2D QCD中筛选和限制的更多信息

More on Screening and Confinement in 2D QCD

通过计算外夸克间的相互作用势，同时对外源进行玻色化并分析组合系统的态，以及对味数N_f进行展开，进一步证明了无质量SU（N_c）玻色化QCD的屏蔽行为.我们写下小说“非阿贝尔Schwinger像”的运动方程的解决方案，计算它们的质量，并认为这种类型的大规模模式的交流与屏蔽机制。大质量动力学费米子的限制使用（ii）和（iii）。通过将点分裂方法应用于标量流，我们给出了N=1超杨-米尔斯理论的屏蔽行为。

Confinement Phase in Carbon-Nanotubes and the Extended Massive Schwinger Model

Carbon nanotube with electric fluxes confined in one dimension is studied. We show that a Coulomb interaction \propto |x| leads to a confinement phase with many properties similar to QCD in 4D. Low-energy physics is described by the massive Schwinger model with multi-species fermions labeled by the band and valley indices. We propose two means to detect this state. One is through an optical measurement of the exciton spectrum, which has been calculated via the 't Hooft-Berknoff equation with the light-front field theory. We show that the Gell-Mann-Oakes-Renner relation is satisfied by a dark e…

QCD中的重标量禁闭

Confinement from a massive scalar in QCD

在四维规范理论中引入了一个与杨-米尔斯项有质量标量耦合的模型。结果表明，色源产生的势由短程库仑相互作用和长程限制部分组成。远离源，标量消失$\sim r^{-1}$，而电势线性发散$\sim r$。直到一个$N_c$ -依赖因子的阶数为1的模型中的张力参数是$gmf$，其中$m$表示标量的质量和$f$是一个耦合标度进入标量-胶子耦合。

二次引力中的大质量鬼场禁闭、偶极方程与多极态

Massive Ghost Confinement, Dipole Equation and Multipole States in Quadratic Gravity

基于明显协变局域正则算子形式主义，研究二次引力中破坏S矩阵幺正性的大质量鬼场禁闭，推导BRST四重态渐近场的偶极方程，经两种协变量子化后发现量子Fock空间由多极态张成。

Duffin-Kemmer-Petiau理论中的非最小矢量耦合和线性势对大质量玻色子的禁闭

On the nonminimal vector coupling in the Duffin-Kemmer-Petiau theory and the confinement of massive bosons by a linear potential

修正了Duffin-Kemmer-Petiau理论中的矢量耦合。结果表明，最小和非最小矢量势下的电荷共轭和时间反转变换的行为不同。特别是，它表明，非最小矢量势已被错误地应用到弹性介子-核散射的描述和非最小矢量势的空间分量的玻色子的约束起着至关重要的作用。将具有非最小向量线性势的DKP方程映射为非相对论谐振子问题，并详细讨论了这类DKP谐振子解的性质。此外，克莱因悖论的不存在和玻色子在非最小矢量相互作用的存在下的本地化进行了讨论。

Magnetic Charge and Photon Mass: Physical String Singularities, Dirac Condition, and Magnetic Confinement

We find exact, simple solutions to the Proca version of Maxwell's equations with magnetic sources. Several properties of these solutions differ from the usual case of magnetic charge with a massless photon: (i) the string singularities of the usual 3-vector potentials become real singularities in the magnetic fields; (ii) the different 3-vector potentials become gauge inequivalent and physically distinct solutions; (iii) the magnetic field depends on $r$ and $θ$ and thus is no longer rotationally symmetric; (iv) a combined system of electric and magnetic charge carries a field angular momentum…

The Schwinger function, confinement and positivity violation in pure gauge QED

The lattice regularized pure gauge compact U(1) theory is an ideal laboratory to explore how confinement is realized as its phase diagram has a confined and a deconfined phase that depends on the value of the coupling constant, i.e. on $β$. Herein, the connection between confinement and positivity violation through the Schwinger function associated with the Landau gauge photon propagator is investigated. The simulations reported show a very clear link between the realization of confinement and positivity violation of the photon Schwinger function and, therefore, of the photon Källén-Lehmann sp…

String tension and robustness of confinement properties of in the Schwinger-Thirring model

Confinement properties of the $1+1$ Schwinger model can bestudied by computing the string tension between two charges. It is finite (vanishing) if the fermions are massive (massless) corresponding to the occurrence of confinement (screening). Motivated by the possibility of experimentally simulate the Schwinger model, we investigate here the robustness of its screened and confined phases. Firstly, we analyze the effect of nearest-neighbour density-density interaction terms, which -- in the absence of the gauge fields -- give rise to the Thirring model. The resulting Schwinger-Thirring model is…

二维 QED 中的轴反常与禁闭：阈值处真空极化的奇异行为

Axial Anomaly and Confinement in Two-dimensional QED: Singular Behavior of Vacuum Polarization at Threshold

本文研究 1+1 维 QED 中真空极化在阈值处的奇异性，结合轴反常与禁闭解释其物理意义，并通过 $e^+e^-\to\mu^+\mu^-$ 截面及玩具版 R 比值说明穿衣光子传播子对获得有限结果的作用。

大质量光子与洛伦兹破坏

Massive photons and Lorentz violation

所有的二次平移和规范不变的光子算符的洛伦兹击穿被包括到施图克尔伯格拉格朗日广义光子规范。精确地确定了相应的色散关系和树级传播子，并导出了一些前阶结果。如何将这种洛伦兹破坏效应纳入微扰量子场展开的问题得到了解决。这些结果在洛伦兹破缺量子场论中的应用包括红外发散的正则化以及大质量矢量玻色子的自由传播。

QCD传播子的解析结构、禁闭与退禁闭

The analytic structure of the QCD propagators, confinement, and deconfinement

利用有质量变形的QCD微扰论（屏蔽有质量展开）在单圈阶计算了零空间动量有限温度朗道规范胶子传播子的解析结构，发现温度从0到约3Tc范围内无退禁闭信号，并指出有质量微扰方法可能因违反QCD Ward恒等式而缺失关键动力学信息。

演生光子与禁闭机制

Emergent photons and mechanisms of confinement

数值研究4D $\mathbb{Z}_N$格点规范理论，证明禁闭相与光子相均由center vortices增殖驱动，关键差异在于monopoles是否大量增殖。

Sine-Gordon模型和有质量Thirring模型的禁闭、孤子和等价性

Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models

考虑具有两个Dirac旋量和三个标量场的二维可积共形不变场论。相互作用将旋量中的双线性项耦合到标量的指数。它的可积性是建立在sl（2）仿射卡茨-穆迪代数的基础上的，它是所谓的共形仿射Toda理论与物质场耦合的一个简单例子。利用玻色化技术，我们证明了U（1）Noether流和拓扑流之间的经典等价性在量子水平上成立，并由此导出了一个类似于袋模型的机制，用于孤子内部旋量场的禁闭.通过玻色化的旋量，我们表明，该理论的sine-Gordon模型和自由标量。我们构造的两个孤子的解决方案，并表明它们的相互作用导致相同的时间延迟的sine-Gordon孤子。该模型提供了一个很好的实验室，以测试对偶思想的背景下的等效之间的正弦戈登和Thirring理论。

五维中的禁闭

Confinement in Five Dimensions

本文利用 M-理论在锥形卡拉比-丘三流形上的几何实现研究五维超共形场论的相结构，证明许多 5d SCFT 可产生带禁闭弦和未破缺 1-形式对称性的有质量禁闭真空，并给出由完备里奇平坦度量参数空间构造的最简单例子。

大质量光子的Stefan-Boltzmann定律

Stefan-Boltzmann law for massive photons

本文将Stefan-Boltzmann定律推广到包括大质量光子。获得正确的辐射公式的一个关键因素是要认识到一个大质量的光子并不以（无质量的）光速传播。因此，与预期相反，辐射率与能量密度乘以光速不成正比。

Infrared Effects and the Soft Photon Theorem in Massive QED

Stueckelberg QED with massive photon is known to be renormalizable. But the limit of the mass going to zero is interesting because it brings the resolution to infrared questions through the role of Stueckelberg field at null infinity in addition to providing new asymptotic symmetries. Such symmetries facilitate the soft photon theorems also.

超曲面邻域内的曲积空间和测地线运动

Warped product spaces and geodesic motion in the neighbourhood of hypersurfaces

研究了五维翘曲乘积空间中非零静止质量试验粒子和光子的经典测地线运动。我们表明，它是可能的，以获得这些运动的一般图片，使用自然解耦，发生在这样的空间之间的运动在第五维和运动的超曲面。这种分裂允许使用相空间分析，以调查可能的限制粒子和光子的超曲面在五维翘曲的产品空间。利用这样的分析，我们发现了一种新的形式的准禁闭，这是振荡和中性稳定。我们还发现，这类翘曲积空间的局部满足Z2对称默认。这种限制的重要性在于它纯粹是由于经典引力效应，而不需要膜型限制机制的存在。

Two-Loop Master Integrals for the Planar QCD Massive Corrections to Di-photon and Di-jet Hadro-production

We present the analytic calculation of the Master Integrals necessary to compute the planar massive QCD corrections to Di-photon (and Di-jet) production at hadron colliders. The masters are evaluated by means of the differential equations method and expressed in terms of multiple polylogarithms and one- or two-fold integrals of polylogarithms and irrational functions, up to transcendentality four.

Bridging the Chiral symmetry and Confinement with Singularity

We consider a holographic quark model where the confinement is a consequence of the quark condensate. Surprisingly, the equation of motion of our holographic model can be mapped to the old spin-less bag model. Both models correctly reproduce the linear Regge trajectory of hadrons for zero quark mass. For the case of non-zero quark mass, the model lead us to Heun's equation. The mass term is precisely the origin of the higher singularity, which changes the system behavior drastically. Our result can shed some light on why the chiral transition is so close to the confinement transition. In the m…

Massive photon propagator in the presence of axionic fluctuations

The theory of massive photons in the presence of axions is studied as the effective theory describing the electromagnetic response of semimetals when a particular quartic fermionic pairing perturbation triggers the formation of charged chiral condensates, giving rise to an axionic superconductor. We investigate corrections to the Yukawa-like potential mediated by massive photons due to axion excitations up to one-loop order and compute the modifications of the London penetration length.