Ivan Arraut
We demonstrate that the number of Nambu-Goldstone bosons is always equal to the number of conserved currents inside the scenario of non-Hermitian field theories with spontaneous symmetry breaking. This eliminates the redundancies which normally appears in Hermitian field theories, specifically when the Lagrangian under analysis violates explicitly the Lorentz symmetry.
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We present explicitly a relation between the Nambu-Goldstone boson and the order parameter in non-relativistic systems with spontaneous symmetry breaking. We show that the Nambu-Goldstone bosons are characterized by transformation property of the order parameter under symmetry transformation of a system. We give an explicit formula for the Nambu-Goldstone boson for a general Lie group $G$, and then the number of the Nambu-Goldstone boson is derived straightforwardly from the symmetry of the order parameter, i.e. the type of symmetry breaking. We show that the Ward-Takahashi identity is modifie…
Nambu-Goldstone bosons and the Higgs mechanism without Lorentz invariance: Analysis based on constrained-system theory
首先，我们将Nambu-Goldstone玻色子的计数定则推广到包含二次导数项的系统。在这种情况下，II型南武-戈德斯通玻色子可能会与大质量的南武-戈德斯通玻色子一起出现。玻色子的数量并没有减少，相反，没有两个时间的导数项的系统。我们还研究了减少的自由度的角度的Dirac-Bergmann理论的约束和重现的计数规则，南武-戈德斯通玻色子没有洛伦兹不变性。然后，我们在Dirac-Bergmann理论的基础上，构造了一般的Higgs模型，并研究了含这些Nambu-Goldstone玻色子的Higgs现象。我们证明了这个系统中的规范场吸收了所有的Nambu-Goldstone玻色子，如I型、II型和大质量玻色子。
Spontaneous Breakdown of the Lorentz Invariance and the Nambu-Goldstone Theorem
在一类三维阿贝尔规范理论中，洛伦兹不变性被动态产生的磁场自发破缺。一个原本具有拓扑质量的光子变成了无间隙的，即在{ \vec p}=0时p_0=0。事实上，光子是与洛伦兹不变性的自发破缺有关的南武-戈德斯通玻色子。虽然由两个洛伦兹助推发生器产生的对称性被打破，但似乎只有一个物理的南武-戈德斯通玻色子，即光子。证明了南武-戈德斯通定理中的沃德恒等式是光子极点饱和的.
Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Massive Modes
在任何具有自发对称性破缺的理论中，解释无质量的南武-戈德斯通模和有质量的希格斯模是很重要的。在这篇简短的评论中，这些模式的命运被检查的情况下，一个大黄蜂模型，其中洛伦兹对称性自发破缺。
On gravitational interaction of spin 3/2 Nambu-Goldstone fermion
构造了自旋为3/2的Nambu-Goldstone（N-G）费米子的新引力相互作用，为自旋为3/2的无质量场的相容引力耦合提供了一个新的框架.在一个新的全局超对称下，作用量是不变的。
This talk focuses on the role of light scalars in cosmology, both Nambu Goldstone bosons and pseudo moduli. The former include QCD axions, which might constitute the dark matter, and more general axions, which, under certain conditions, might play the role of inflatons, implementing {\it natural inflation}. The latter are the actors in (generalized) hybrid inflation. They rather naturally yield large field inflation, even mimicking chaotic inflation for suitable ranges of parameters.
Effective Couplings of Dynamical Nambu-Goldstone Bosons with Elementary Fermions
假设无标量场的无质量规范理论的手征对称性动力学自发破缺，我们找到了一种利用辅助场构造动力学南武-戈德斯通玻色子和元素费米子的有效作用量的方法。在这里，动力学粒子被假定为由基本费米子组成。包括衰减常数在内的各种量都是从这个有效作用中计算出来的。
Nambu-Goldstone Fields, Anomalies and WZ Terms
我们构造的Wess-Zumino条款从异常的情况下，拟群为以下情况。一个是与自发破缺的整体对称性有关的南武-戈德斯通场的有效规范场理论，另一个是反常规范理论。我们将发展的形式主义可以看作是李群的非线性实现方法的推广。作为一个例子，我们考虑2D重力与Weyl不变正则化
NAMBU-GOLDSTONE BOSON ON THE LIGHT-FRONT
在离散光阵面量子化的框架下研究了连续对称性的自发击穿。我们考虑3+1维线性西格玛模型，并表明，零模的仔细处理，以及通过引入NG玻色子质量的理论的正则化，导致正确的描述Nambu-Goldstone相位的光阵面。
We investigate dispersion relation of Nambu-Goldstone modes in a dissipative system realized by the AdS/CFT correspondence. We employ the D3/D7 model which represents ${\cal N} = 4$ supersymmetric Yang-Mills theory coupled to ${\cal N = 2}$ flavor fields. If we consider massless quarks in the presence of an external magnetic field, the system exhibits the phase transition associated with the spontaneous symmetry breaking of the chiral symmetry. We find that the Nambu-Goldstone modes shows a diffusive behavior in the dispersion relation, which agrees with that found with the effective field the…
$U_L(N)\times U_R(N)$-invariant four-fermion interactions and Nambu-Goldstone mechanism at finite temperature
在NJL形式的手征$U_L(N)\times U_R(N)$费米子模型中，证明了如果假设所有费米子都具有相等的质量和相等的化学势，则在低于对称性恢复温度$T_c$的有限温度$T$处，将存在$N^2$有质量的标量复合粒子和$N^2$无质量的赝标复合粒子（Nambu-Goldstone玻色子）.这表明有限温度下自发对称破缺$U_L(N)\times U_R(N) \to U_{L+R}(N)$的Goldstone定理与该模型中热场论的实时形式一致。
New supersymmetry algebra on gravitational interaction of Nambu-Goldstone fermion
研究了SGM作用量作为N-G费米子引力耦合的时空对称性。新的非线性超对称变换（NL-SUSY）的算符构成了一个封闭代数，它揭示了N-G费米子（NL-SUSY）的性质和一个推广的一般坐标变换。本文还引入了一个广义局部洛伦兹变换，它构成一个闭代数.
Moduli Space of Global Symmetry in N=1 Supersymmetric Theories and the Quasi-Nambu-Goldstone Bosons
在N=1的超对称理论中，我们导出了整体对称的模空间。我们表明，在一般的点，它与准Nambu-Goldstone（QNG）玻色子的空间相吻合，除了普通的Nambu-Goldstone（NG）玻色子时，全球对称性G自发地打破了它的子群H保持N=1超对称。在奇点处，大部分NG玻色子转变为QNG玻色子，整体对称性增强。由NG玻色子参数化的G轨道是模空间上的纤维，奇点对应于G轨道中H轨道的收缩点。我们还证明了低能有效拉格朗日量是轨道图的任意函数。
Partial Breaking of N=2 Supersymmetry and Decoupling Limit of Nambu-Goldstone Fermion in U(N) Gauge Model
本文研究了N=2超对称自发破缺得到的N=1 U（N）规范模型。N=2作用量中包含的Fayet-Iliopoulos项在N=1真空中不出现，超势被修正以破坏离散R对称性.我们取一个极限，在这个极限中，卡勒度规变得平坦，超势保持非平凡的形式。南武-戈德斯通费米子与其他场解耦，但产生的作用量仍然是N=1超对称的。它揭示了N=1 U（N）规范理论中费米子位移对称性的起源。
Composite antisymmetric-tensor Nambu-Goldstone bosons in a four-fermion interaction model and the Higgs mechanism
从双味't Hooft相互作用的Fierz变换出发（一个四费米子拉格朗日量与反对称洛伦兹张量相互作用项增加了一个NJL型洛伦兹标量相互作用负责动力学对称性破缺和夸克质量产生），我们表明：（1）当标量耦合与张量耦合成二比一时，出现反对称张量Nambu-Goldstone玻色子，该比值自然地出现在双味't Hooft相互作用的Fierz变换中;（2）耦合到该系统的非阿贝尔矢量规范玻色子获得非零质量。轴向矢量场不与反对称张量场混合，因此那里没有质量移动。
Nambu-Goldstone Mechanism in Real-Time Thermal Field Theory
在电弱对称性破缺的一代费米子凝聚方案中，基于实时热场论中的Schwinger-Dyson方程，在费米子泡图近似下证明了：在低于对称性恢复温度$T_c$的有限温度$T$下，一个巨大的希格斯玻色子和三个无质量的南武-Goldstone玻色子可以从电弱群$SU_L(2)\times U_Y(1) \to U_Q(1)$的自发破缺中产生，如果一代中的两个费米子味是质量简并的，因此，Goldstone定理在这种情况下严格有效。然而，如果两个费米子味具有不相等的质量，由于“热flactuation”，戈德斯通定理将仅在零温费米子圈中的非常大的动量截止$Λ$或低能标度下近似为真。所有可能的箍缩奇点被证明是相互抵消，如预期的实时热场论。
We demonstrate that when there is spontaneous symmetry breaking in any system, relativistic or non-relativistic, the dynamic of the Nambu-Goldstone bosons is governed by the Quantum Yang-Baxter equations. These equations describe the triangular dynamical relations between pairs of Nambu-Goldstone bosons and the degenerate vacuum. We then formulate a theorem and a corollary showing that these relations guarantee the appropriate dispersion relation and the appropriate counting for the Nambu-Goldstone bosons.
We explain the origin of the mass for the Nambu-Goldstone bosons when there is a chemical potential in the action which breaks explicitly the symmetry. The method is based on the number of independent histories for the interaction of the pair of Nambu-Goldstone bosons with the degenerate vacuum (triangle relations). The analysis suggests that under some circumstances, pairs of massive Nambu-Goldstone bosons can become a single degree of freedom with an effective mass defined by the superposition of the individual masses of each boson. Possible mass oscillations for the Nambu-Goldstone bosons a…
We study an $O(N)$ scalar model under shear flow and its Nambu-Goldstone modes associated with spontaneous symmetry breaking $O(N) \to O(N-1)$. We find that the Nambu-Goldstone mode splits into an infinite number of gapless modes, which we call the rainbow Nambu-Goldstone modes. They have different group velocities and the fractional dispersion relation $ω\sim k_1^{2/3}$, where $k_1$ is the wavenumber along the flow. Such behaviors do not have counterparts in an equilibrium state.
We discuss a supersymmetric extension of a non-relativistic Chern-Simons matter theory, known as the SUSY Jackiw-Pi model, in a harmonic trap. We show that the non-relativistic version of the superconformal symmetry, called the super-Schrödinger symmetry, is not spoiled by an external field including the harmonic potential. It survives as a modified symmetry whose generators have explicit time dependences determined by the strength of the trap, the rotation velocity of the system and the fermion number chemical potential. We construct 1/3 BPS states of trapped Jackiw-Pi vortices preserving a p…
Quantum Mechanics Violating Effects to Masses of Nambu-Goldstone Bosons: A Lesson for Majoron
以Majoron为例，研究了引力量子力学违反（QMV）对Nambu-Goldstone玻色子质量的影响。我们表明，超对称majoron的质量为O（keV）的5维潜在的或更小的质量与更高的维度有效的潜力。我们扩展了Dashen的伪Nambu-Goldstone玻色子的公式，包括QMV的可能影响。
Pseudo-Nambu-Goldstone bosons and tachyons in flux compactification
研究磁通量紧化规范理论中的对称性破缺谱，提出双 $U(1)$ 赝 Nambu-Goldstone 标量并证明 $SU(2)$ 伴随标量可在大耦合下消除快子且保持手征性。
Linearizing N = 1 nonlinear supersymmetry with higher derivative terms of a Nambu-Goldstone fermion
本文研究了N = 1超对称性（SUSY）下线性超对称性的标量超多重态与非线性（NL）超对称性模型之间的关系，该模型除了包含Nambu-Goldstone（N-G）费米子的V-A作用量外，还包含明显病态的高阶导数项.通过启发式论证，构造了连接线性和NL超对称模型的N-G费米子高阶导数超对称不变量关系。本文讨论了N-G费米子在NL超对称模型中的高阶导数作用量，它显然包含一个（外尔）鬼场。利用这一关系，我们还明确地证明了标准NL SUSY V-A模型与我们的NL SUSY模型之间的等价性，并以病态高阶导数为例，证明了NL SUSY与N-G费米子作用的普适性.
Nambu-Goldstone dynamics and generalized coherent-state functional integrals
本文给出了在自发破缺理论中攻击Nambu-Goldstone动力学的一种新方法。由于南武-戈德斯通场的目标空间是一个群陪集空间，它们的有效量子动力学可以很自然地用广义相干态泛函积分来表述。作为这条推理线的一个明确的例子，我们构造了一个低能量的有效拉格朗日的海森堡铁磁体在断相。在WKB近似下的主导场位形导致量子铁磁体的Landau-Lifshitz方程。相应的线性化方程允许识别Nambu-Goldstone玻色子与铁磁磁振子。
Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation
我们分析了自洽相对论变分高斯波泛函近似无自旋场论的南武-戈德斯通[NG]定理的群论分支。在一个说明性的例子中，我们展示了如何南武-戈德斯通定理将工作在O（N）对称$ϕ^4$标量场理论，如果真空的剩余对称性小于O（N-1），例如，如果真空是O（N-2），或O（N-3），.对称的[This并不意味着任何一个“较小”的真空实际上是绝对能量最小值：稳定性分析还没有做过。所需的NG玻色子的数量是（2N - 3），或（3 N- 6），.分别，这可能超过N，在拉格朗日的基本字段的数量。我们展示了所需的新NG玻色子如何出现在通道中，即使通道中的量子数与拉格朗日量中的N个“基本粒子“（标量场量子，或Castillejo-Dalitz-Dyson [CDD]极点）中的一个不相同，即在那些没有CDD极点的“味道”通道中。相应的南武-戈德斯通玻色子是一对质量基本（CDD）标量场激发的复合物（束缚态）。作为这种方法的一个非平凡的例子，我们将其应用到物理上更有趣的“t Hooft $σ$模型（一个扩展的$N_{f} = 2$玻色子线性$σ$模型，具有四个标量场和四个赝标量场），具有自发和显式破缺的手征$O(4) \times O(2) \simeq SU_{\rm R} (2) \times SU_{\rm L}(2) \times U_{\rm A}(1)$对称性。
In non-relativistic systems, when there is spontaneous symmetry breaking, the number of Nambu-Goldstone bosons ($n_{NG}$) are not necessarily equal to the number of broken generators ($n_{BG}$). Here we use the method of operators for analyzing the necessary conditions in order to obtain the correct dispersion relation for the Nambu-Goldstone bosons.
Counting rule for Nambu-Goldstone modes in nonrelativistic systems
本文用Mori投影算符方法讨论了零温和有限温非相对论系统中Nambu-Goldstone模的计数规则。我们证明了Nambu-Goldstone模的个数等于破缺电荷数Q_a减去[Q_a，Q_b]期望值秩的一半。
Nambu-Goldstone mechanism at finite temperature in the imaginary-time and real-time formalism
在热场论的双时形式和实时形式下，通过对四点函数矩阵对角化，重新定义了标量束缚态的物理传播子，在费米子泡图近似下的Schwinger-Dyson方程的基础上，重新研究了一代费米子凝聚方案中的Nambu-Goldstone电弱对称性破缺机制，并比较所得结果。我们得到的结论是，在这两种形式中，自发电弱对称破缺的Goldstone定理对质量简并的两种费米子严格成立，而对质量非简并的费米子仅在低能标度下近似成立，尽管这两种形式在标量束缚态的传播子的虚部上存在一些差异.当两种费米子的质量不相等时，如果零温环中的动量截止足够大，则Higgs粒子可能的涨落效应可以忽略不计。所有的结果表明，在目前讨论的问题中的两个形式主义的物理等价性。
Nambu-Goldstone modes in segregated Bose-Einstein condensates
从理论上研究了不互溶双组分玻色-爱因斯坦凝聚体中的Nambu-Goldstone模。在均匀系统中，平坦的畴壁被稳定化，在两个复序参量的存在下，除了两个U（1）对称性破缺外，垂直于畴壁的平移不变性也自发破缺.我们阐明了低能激发的性质，并确定存在两种Nambu-Goldstone模：具有线性色散的同相声子和具有分数色散的ripplon。特征色散的签名可以在谐波势中的分离凝聚体中得到验证。
We study a scalar zero mode originated from extradimensional components of a gauge field in a six-dimensional theory compactified on a magnetized torus. We confirm it is a Nambu-Goldstone boson of the translational symmetry on the torus which is breaking spontaneously due to magnetic flux. We also show explicitly it is massless up to the two-loop level. Moreover, we discuss full order contributions by considering the effective potential.
We discuss spontaneous symmetry breaking of open classical and quantum systems. When a continuous symmetry is spontaneously broken in an open system, a gapless excitation mode appears corresponding to the Nambu-Goldstone mode. Unlike isolated systems, the gapless mode is not always a propagation mode, but it is a diffusion one. Using the Ward-Takahashi identity and the effective action formalism, we establish the Nambu-Goldstone theorem in open systems, and derive the low-energy coefficients that determine the dispersion relation of Nambu-Goldstone modes. Using these coefficients, we classify …
Nambu-Goldstone explosion under brane perforation
我们表明，穿孔的三膜的质量撞击它从五维散装激发南武-戈德斯通球面波向外传播的光的速度。据推测，这种效应可能会在膜世界宇宙学模型中引起“无动机的”能量释放事件。
We investigate the existence of double copy structure, or the lack thereof, in higher derivative operators for Nambu-Goldstone bosons. At the leading ${\cal O}(p^2)$, tree amplitudes of Nambu-Goldstone bosons in the adjoint representation can be (trivially) expressed as the double copy of itself and the cubic bi-adjoint scalar theory, through the Kawai-Lewellen-Tye bilinear kernel. At the next-to-leading ${\cal O}(p^4)$ there exist four operators in general, among which we identify one operator whose amplitudes exhibit the flavor-kinematics duality and can be written as the double copy of ${\c…
Geometry of Classical Nambu-Goldstone Fields
本文提出坐标无关的一阶有效场论几何表述，将Nambu-Goldstone场视为伴丛截面，仅凭对称性推导其数目与类型，并揭示洛伦兹破缺序参量在分类中引入辛结构的关键作用。
Nambu-Goldstone Modes in Gravitational Theories with Spontaneous Lorentz Breaking
洛仑兹对称性的自发破缺被认为是一种可能的机制，可能发生在基本普朗克尺度理论的背景下，如弦论或引力的量子理论。然而，如果洛仑兹对称性自发破缺，两组问题立即出现：南武-戈德斯通模式的命运是什么，希格斯机制会发生吗？这里简要介绍了最近研究这些问题的一些工作。
We study the soft behavior of two seemingly different particles that are both referred to as dilatons in the literature, namely the one that appears in theories of gravity and in string theory and the Nambu-Goldstone boson of spontaneously broken conformal invariance. Our primary result is the discovery of a soft theorem at subsubleading order for each dilaton, which in both cases contains the operator of special conformal transformations. Interesting similarities as well as differences between the dilaton soft theorems are discussed.
Masses of the pseudo-Nambu-Goldstone bosons in two flavor color superconducting phase
本文利用Cornwall-Jackiw-Tomboulis有效作用量估计了具有两种轻味的致密QCD色超导相中赝Nambu-Goldstone玻色子的质量。从参数上讲，与超导能隙的值相比，耦合常数的幂抑制了二重态和反二重态玻色子的质量。这与单重态伪南武-戈德斯通玻色子的质量表达式有质的不同，后者是由非微扰效应引起的。我们认为（反）二重态伪Nambu-Goldstone玻色子[相对于未破缺的SU（2）_{c}]形成无色的类粲偶素束缚态。并估算了相应的结合能。
We propose a pseudo-Nambu-Goldstone inflation where twin waterfall fields coupled to the inflaton are responsible for the graceful exit from inflation by a waterfall transition. In this scenario, the $Z_2$ symmetry for the waterfall fields and the inflaton protects the inflaton potential against dangerous quantum corrections coming from the waterfall couplings. We show that there is a wide range of natural model parameters and initial conditions for a successful inflation and discuss the reheating process by the perturbative decay of the waterfall field with a $Z_2$ invariant Higgs portal. We …
We study quantum antiferromagnetic Heisenberg models on a hypercubic lattice. We prove the following three theorems without any assumption: (i) The spontaneous magnetization which is obtained by applying the infinitesimally weak symmetry breaking field is equal to the maximum spontaneous magnetization at zero or non-zero low temperatures. (ii) When the spontaneous magnetization is non-vanishing at zero temperature, there appears a gapless excitation, Nambu-Goldstone mode, above an infinite-volume pure ground state. (iii) When the spontaneous magnetization is non-vanishing at zero or non-zero l…
Redundancies in Nambu-Goldstone Bosons
我们提出了一个简单的标准，以确定当Nambu-Goldstone玻色子（NGB）的不同对称性是多余的。它解决了一个古老的谜团，为什么晶体有声子自发破坏的翻译，但没有无隙激发同样自发破坏的旋转。类似地，对于超流体，伽利略对称性自发破缺的NGB与声子是多余的。最不平凡的例子是超流体中涡旋晶格的Tkachenko模式，其中声子对于Tkachenko模式是冗余的，被识别为Boboliubov模式。
Geometric pairing of Nambu--Goldstone modes in spacetime symmetry breaking
研究时空对称性破缺系统中Goldstone场的几何配对机制，提出基于Berry曲率的计数公式，并在双组分BEC模型中验证了配对产生二次色散NGM。
We discuss the counting of Nambu-Goldstone (NG) modes associated with the spontaneous breaking of higher-form global symmetries. Effective field theories of NG modes are developed based on symmetry breaking patterns, using a generalized coset construction for higher-form symmetries. We derive a formula of the number of gapless NG modes, which involves expectation values of the commutators of conserved charges, possibly of different degrees.
Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
利用有效拉格朗日方法，我们澄清了没有洛伦兹不变性的南武-戈德斯通玻色子的一般问题。我们展示了如何计算它们的数量和研究它们的色散关系。当它们中的一些形成正则共轭对时，它们的数目小于破缺生成元的数目。当生成元的换流子的期望值不为零时，就会发生配对。对于非半单代数，中心扩张是可能的。陪集空间的基本几何一般是部分辛的。
Quark matter at high density may exhibit color superconductivity. As magnetic flux tubes in metallic superconductors, color magnetic flux tubes as non-Abelian vortices appear in the color-flavor locked phase of high density QCD. ${\mathbb C}P^2$ Nambu-Goldstone bosons and Majorana fermions belonging to the triplet representation are known to be localized around a non-Abelian vortex. In this paper, we determine the coupling of these bosonic and fermionic modes by using the nonlinear realization method.
Motivated by recent constructions of TeV-scale strongly-coupled dynamics, either associated with the Higgs sector itself as in pseudo-Nambu-Goldstone boson (pNGB) Higgs models or in theories of asymmetric dark matter, we show that stable solitonic Q- balls can be formed from light pion-like pNGB fields carrying a conserved global quantum number in the presence of the Higgs field. We focus on the case of thick-wall Q-balls, where solutions satisfying all constraints are shown to exist over a range of parameter values. In the limit that our approximations hold, the Q-balls are weakly bound and p…
Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity
研究了自发洛伦兹破坏引起的南武-戈德斯通模的命运。使用的vierbein形式主义，它表明，多达10个洛伦兹和单态Nambu-Goldstone模式可以出现，它们包含在10个模式的vierbein与规范自由度在洛伦兹不变理论。一个一般的治疗自发的局部洛伦兹和单态违反给出了各种时空，和命运的南武-戈德斯通模式被证明取决于时空的几何形状和动力学的张量场触发自发洛伦兹违反。结果说明在一般类的大黄蜂模型涉及真空值的矢量场。在闵可夫斯基和黎曼时空中，大黄蜂模型提供了一个动力学理论，产生一个光子作为南武-戈德斯通玻色子的自发洛伦兹破坏。麦克斯韦和爱因斯坦-麦克斯韦作用量在轴向规范中自动恢复。潜在的实验相关性的相关影响包括在标准模型扩展和非常规的洛伦兹不变耦合的物质和引力部门违反洛伦兹耦合。在黎曼-嘉当时空中，也可能存在希格斯机制的自旋连接，导致传播的南武-戈德斯通模被吸收到引力场的扭转分量中。
Massive Nambu-Goldstone Bosons
Nicolis和Piazza最近指出在有限密度的相对论系统中存在Nambu-Goldstone类激发，其能隙由化学势和对称代数精确确定.我们发现，这种现象是更普遍的比预期的，并证明存在这样的模式在一些系统中从（反）铁磁体在磁场的超流相的量子色动力学。此外，我们证明了这些大规模的Nambu-Goldstone玻色子的计数规则，并构建了一个低能量的有效拉格朗日函数，捕捉他们的动态。
Calculation of Particle Production by Nambu Goldstone Bosons with Application to Inflation Reheating and Baryogenesis
对势场中标量场的粒子产生进行了半经典计算。我们专注于特定的情况下，生产费米子的南部戈德斯通玻色子$θ$。我们导出了考虑粒子反作用的$θ$ -场的（非）定域运动方程。该方程在某些特殊情况下求解，即对于纯Nambu-Goldstone玻色子和倾斜势$ U(θ) \propto m^2 θ^2 $。增强生产的玻色子由于参数共振的影响，我们认为，共振可能会消失时，宇宙的膨胀。本文还介绍了粒子产生工作在再加热中的应用以及暴胀中重子产生的设想。
Kelvin modes as Nambu-Goldstone modes along superfluid vortices and relativistic strings: finite volume size effects
通过构造Kelvin模和平移零模的低能有效理论，分别研究了超流体中沿量子涡旋和相对论整体弦激发的Kelvin模和平移零模以及相对论场论.我们发现，只有在无限体积极限下，它们才成为精确的无隙Nambu-Goldstone模。另一方面，在相对论理论中，我们发现在有限体积系统中，存在一个假想的质量能隙，导致了在临界波长以上的快子不稳定性。我们还发现在非相对论理论中，波长大于某个临界值的开尔文模的传播方向与波长较短的开尔文模的传播方向相反，这与传统的理解相反。Nambu-Goldstone模的数量也使相对论和非相对论理论的Nielsen-Chadha不等式的相等性饱和。
Spontaneous Symmetry Breaking with Abnormal Number of Nambu-Goldstone Bosons and Kaon Condensate
我们描述了一类相对论模型，将有限密度的物质中，连续对称性的自发击穿导致较少数量的南武-戈德斯通玻色子比所需的戈德斯通定理。这门课，特别是，描述了在高密度QCD色香味锁定相位的K介子凝聚的动力学。我们描述了在这个动态的低能量激发的频谱，并表明，尽管存在的冷凝物和无隙激发，这个系统是不是一个超流体。
Can the Nambu-Goldstone Boson Live on the Light-Front?
通过引入显式破缺的NG玻色子质量$m_π$，我们证明了只有在正则化理论的条件下，限制在光阵面（LF）上的NG玻色子才能存在.在LF上积分时，NG玻色子零模在$m^2_π\rightarrow 0$的对称极限中必须具有奇异行为$\sim 1/m^2_π$。在离散化LF量化的线性$σ$模型中的零模式约束，澄清了这一特点。LF电荷湮灭真空，而它在NG相的对称极限中不守恒。
Pseudo-Nambu-Goldstone Dark Matter in Flux Compactification
该研究提出了一种基于六维规范理论紧致化的伪Nambu-Goldstone暗物质模型，通过Wilson线标量场作为DM候选者，无需额外场即可满足热 relic 密度要求并规避直接探测限制。
Nambu-Goldstone bosons with fractional-power dispersion relations
我们确定了超流-超流界面中畴壁涨落的一种特殊色散关系，即所谓的ripplon的起源。由于有效拉格朗日量的非定域性，ripplon具有色散关系$ω\propto k^{3/2}$，这是由体中的无隙超流声子介导的。我们指出了与二维维格纳晶体中纵声子的类比。
These lectures provide an introduction to the low-energy dynamics of Nambu-Goldstone fields, associated with some spontaneous (or dynamical) symmetry breaking, using the powerful methods of effective field theory. The generic symmetry properties of these massless modes are described in detail and two very relevant phenomenological applications are worked out: chiral perturbation theory, the low-energy effective theory of QCD, and the (non-linear) electroweak effective theory. The similarities and differences between these two effective theories are emphasized, and their current status is revie…
Optimized Perturbation Theory at Finite Temperature --- Renormalization and Nambu-Goldstone theorem in O(N) phi^4 Theory ---
利用O（N）phi^4理论和自发对称性破缺，评述了作者最近发展的有限温度优化微扰理论。该方法在高$T$下自动求和较高的环（包括硬热环），同时在相对低的$T$下解决了快子极点问题。我们证明了（i）紫外发散的重整化可以在任意给定的OPT阶中系统地进行，（ii）Nambu-Goldstone定理对任意的$N$和任意给定的OPT阶都是成立的.
In massless QCD coupled to QED in an external magnetic field, a photon with the linear polarization in the direction of the external magnetic field mixes with the charge neutral pion through the triangle anomaly, leading to one gapless mode with the quadratic dispersion relation $ω\sim k^2$ and one gapped mode. We show that this gapless mode can be interpreted as the so-called type-B Nambu-Goldstone (NG) mode associated with the spontaneous breaking of generalized global symmetries and that its presence is solely dictated by the anomalous commutator in the symmetry algebra. We also argue a pos…
Non-relativistic Nambu-Goldstone modes associated with spontaneously broken space-time and internal symmetries
我们证明了在非相对论性理论中，当存在拓扑孤子时，平移对称的动量算符不可能与内部对称算符交换。在O（3）西格玛模型中，在具有易磁化轴的铁磁体的磁畴壁附近，出现了由平移模和内零模组成的具有二次色散的Nambu-Goldstone耦合模。
Photons emerging as Goldstone bosons from spontaneous Lorentz symmetry breaking: The Abelian Nambu model
在把流守恒和高斯定律作为初始条件加到阿贝尔Nambu模型上之后，我们证明了所得到的理论等价于非线性规范$\left(A_{μ}A^{μ}-n^{2}M^{2}\right)=0$中的标准QED，等价于微扰论中的所有阶。我们表明，这两个模型中的相同的变量，产生相同的费曼规则的相互作用和传播。关键的一点是验证QED扇区中规范固定过程产生的Faddeev-Popov鬼与所有阶次解耦。我们验证了这种解耦的方法，如杨米尔斯理论调查轴向应变片的行为。这两个理论之间的等价性支持了规范粒子可以被设想为起源于自发洛伦兹对称破缺的戈德斯通玻色子的观点。
Linear space of spinor monomials and realization of the Nambu-Goldstone fermion in the Volkov-Akulov and Komargodski-Seiberg Lagrangians
本文讨论了作者提出的描述Nambu-Goldstone（NG）费米子的Komargodski-Seiberg（KS）作用量和Komov-Akulov（VA）作用量的解析匹配算法。解释了算法的本质，证明了算法的一致性，并再现了最近在计算机辅助下得到的结果，当考虑到适当的Fierz重排的Majorana bispinors。我们揭示了一个线性空间的复合旋量单项式$Δ_{m}$是解决方案的标量约束$(\partial^{m}\barψΔ_{m})=0$。这个空间是用来澄清的NG费米子场$ψ$的KS和VA实现之间的关系。
The Gross-Pitaevskii (GP) or nonlinear Schrödinger equation relevant to ultracold atomic gaseous Bose-Einstein condensates possess a modified Schrödinger symmetry in two spatial dimensions, in the presence of a harmonic trapping potential, an (artificial) constant magnetic field (or rotation) and an electric field of a quadratic electrostatic potential. We find that a variance and a center of a trapped gas with or without a vorticity can be regarded as massive Nambu-Goldstone (NG) modes associated with spontaneous breaking of the modified Schrödinger symmetry. We show that the Noether theorem …
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