Adrian Tanasa
We review here the construction of a translation-invariant scalar model which was proved to be perturbatively renormalizable on Moyal space. Some general considerations on nonlocal renormalizability are given. Finally, we present perspectives for generalizing these quantum field theoretical techniques to group field theory, a new setting for quantum gravity.
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Translation-invariant noncommutative gauge theories are discussed in the setting of matrix modeled gauge theories. Using the matrix model formulation the explicit form of consistent anomalies and consistent Schwinger terms for translation-invariant noncommutative gauge theories are derived.
A matrix modeling formulation for translation-invariant noncommutative gauge theories is given in the setting of differential graded algebras and quantum groups. Translation-invariant products are discussed in the setting of α-cohomology and it is shown that loop calculations are entirely determined by α-cohomology class of star product in all orders. Noncommutative version of geometric quantization and (anti-) BRST transformations is worked out which leads to a noncommutative description of consistent anomalies and Schwinger terms.
A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar and nonplanar axial anomalies are obtained.
Scalar and gauge translation-invariant noncommutative models
我们在这里做一个简短的概述，最近的事态发展，关于非交换Moyal空间的不变性模型。首先提出了一个标量模型，并证明了可重正化。计算了它的单圈重整化群流和参数表示。此外，最近给出了一种获取其交换极限的机制。最后，提出了一个可重整化的、守恒不变的规范模型。
Exact renormalization of a noncommutative ϕ^3 model in 6 dimensions
6维的非对易自对偶模型被量子化，并通过将其映射到孔采维奇模型而得到本质上的解决。该模型被证明是可重正化的和渐近自由的，和可解的属属。它需要波函数和耦合常数重整化。裸参数的精确（全阶）重整化被明确地确定，这原来只依赖于属0扇区。运行的耦合常数也被精确计算，它比单回路β函数预测的下降得更快。发现了向不稳定相的相变。
We construct here the parametric representation of a translation-invariant renormalizable scalar model on the noncommutative Moyal space of even dimension $D$. This representation of the Feynman amplitudes is based on some integral form of the noncommutative propagator. All types of graphs (planar and non-planar) are analyzed. The rôle played by noncommutativity is explicitly shown. This parametric representation established allows to calculate the power counting of the model. Furthermore, the space dimension $D$ is just a parameter in the formulas obtained. This paves the road for the dimensi…
Renormalization of the noncommutative phi^3 model through the Kontsevich model
我们指出，非对易自对偶phi^3模型可以映射到孔采维奇模型，只要适当地选择后者的特征值。这允许将已知的Kontsevich模型的结果应用于场论的量子化，特别是KdV流和维拉索罗约束。2维的情况下，制定明确。我们得到了自由能和一些n点函数的亏格展开式的非微扰表达式。有限耦合的完全重整化，这是由亏格0部门只。任何n点函数的亏格展开式中的所有贡献在重整化后都是有限的。确定了一个临界耦合，超过该临界耦合，模型是不稳定的。该模型没有UV/IR疾病。
Random noncommutative geometry can be seen as a Euclidean path-integral approach to the quantization of the theory defined by the Spectral Action in noncommutative geometry (NCG). With the aim of investigating phase transitions in random NCG of arbitrary dimension, we study the non-perturbative Functional Renormalization Group for multimatrix models whose action consists of noncommutative polynomials in Hermitian and anti-Hermitian matrices. Such structure is dictated by the Spectral Action for the Dirac operator in Barrett's spectral triple formulation of fuzzy spaces.The present mathematical…
We report on a comprehensive analysis of the renormalization of noncommutative ϕ^4 scalar field theories on the Groenewold-Moyal (GM) plane. These scalar field theories are twisted Poincaré invariant. Our main results are that these scalar field theories are renormalizable, free of UV/IR mixing, possess the same fixed points and β-functions for the couplings as their commutative counterparts. We also argue that similar results hold true for any generic noncommutative field theory with polynomial interactions and involving only pure matter fields. A secondary aim of this work is to provide a co…
One-loop $β$ functions of a translation-invariant renormalizable noncommutative scalar model
最近，Moyal空间上一类新的可重整化$ϕ^{\star 4}_{4}$标量模型被证明是微扰可重整化的.它是不变量，并在动作中引入了一个$a/(θ^2p^2)$项。我们在这里计算的$β$和$γ$功能在一个循环的水平，为这个模型。证明了耦合常数$β_λ$函数与交换$\mathbb{R}^4$上的$ϕ^4$模型具有相同的行为。还计算新参数$a$的$β_a$函数。对这些结果进行了解释。
It is shown that the $n$-point functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not provide a connection to the popular traditional Euclidean approach to noncommutative field theory (unless the time variable is assumed to commute). Instead, one finds Schwinger functions with twistings involving only momenta that are on the mass-shell. This explains why renormalization in the traditional Euclidean noncommutative framework crudely differs from …
Renormalization of noncommutative phi 4-theory by multi-scale analysis
本文给出了四维Moyal平面上的实欧几里德φ 4-模型对所有阶可重整化的一个更有效的证明。我们证明了传播子的严格界，完成了以前的重正化证明的基础上的非局部矩阵模型的重整化群方程。另一方面，我们的边界允许一个强大的多尺度分析所产生的带状图。在这里，对偶图起着特殊的作用，因为角动量守恒在对偶图中很方便地表示出来。在对偶图中根据尺度属性选择生成树，证明了循环角动量的求和可以在没有代价的情况下进行，从而使功率计算简化为传播子数与对偶图中完全内顶点数的平衡.
Renormalization of noncommutative U(N) gauge theories
给出了非对易U（N）规范理论是单圈可重整化的一个明确证明
Renormalization of noncommutative Yang-Mills theories: A simple example
通过计算证明了非对易Yang-Mills理论中由任意多个单圈鬼传播子修正重复插入到自身中所构成的Feynman图是局部反项可重正化的.这为该模型的可重正化性猜想提供了强有力的支持。
Topological structure of translation-invariant noncommutative Yang-Mills theories are studied by means of a cohomology theory, so called star-cohomology, which plays an intermediate role between de Rham and cyclic (co)homology theory for noncommutative algebras and gives rise to a cohomological formulation comparable to Seiberg-Witten map.
We show that gauge-independent terms in the one-loop and multi-loops $β$-functions of the Standard Model can be exactly computed from the Wetterich functional renormalization of a matrix model. Our framework is associated to the finite spectral triple underlying the computation of the Standard Model Lagrangian from the spectral action of Noncommutative Geometry. This matrix-Yukawa duality for the $β$-function is a first hint towards understanding the renormalization of the Noncommutative Standard Model conceptually, and provides a novel computational approach for multi-loop $β$-functions of pa…
Noncommutative Translations and $\star$-Product Formalism
考虑具有李代数非对易性的非对易时空（如$κ$ -变形Minkowski空间）.在经典域的框架下，我们推广了$\star$ -积，以便用交换的形式来表示非交换的平移。证明了非对易双线性作用在非对易场的局部积下的平移不变性。对二次非交换性也作了简要的讨论。
Symmetries and Renormalization of Noncommutative Field Theory
综述了非对易场论的重整化和时空对称性的实现的最新进展，并认为它们是密切相关的。
Introduction to Hopf algebras in renormalization and noncommutative geometry
我们回顾了在量子场论的重整化和在非对易几何中对指数计算很重要的框架丛的超同态的研究中的Hopf代数的出现。
The one-loop renormalization of the gauge sector in the noncommutative standard model
在本文中，我们构建了一个版本的标准模型规范扇区的非对易时空，这是一个单圈重整化的一阶展开中的非对易性参数$θ$。单圈重正化是通过Seiberg-Witten重新定义的非对易规范势的模型包含通常的第一代物质场的六个表示。
We elaborate in this paper a translation-invariant model for fermions in 4-dimensional noncommutative Euclidean space. The construction is done on the basis of the renormalizable noncommutative translation-invariant Phi4 theory introduced by R. Gurau et al. We combine our model with the scalar model, in order to study the noncommutative pseudo-scalar Yukawa theory. After we derive the Feynman rules of the theory, we perform an explicit calculation of the quantum corrections at one loop level to the propagators and vertices.
In this paper we show the renormalizability of the translation invariant noncommutative Chern-Simons theory, motivated by the work done on noncommutative scalar field theory [06]. We add a new term to the bilinear part of the action. In addition, we prove, the finiteness of the theory at one- and two-loop level despite this modification. Finally we perform the one-loop two point functions of the gluon contribution.
Hopf Algebras, Renormalization and Noncommutative Geometry
我们探讨了与QFT重整化相关联的Hopf代数和与叶理横向指数理论的NCG计算相关联的Hopf代数之间的关系。
It has been conjectured in the literature that renormalizability of the $θ$-expanded noncommutative gauge theories improves when one takes into account full nonuniqueness of the Seiberg-Witten expansion, which relates noncommutative (`high-energy') with commutative (`low-energy') fields. In order to check this conjecture we analyze renormalizability of the noncommutative chiral electrodynamics: we quantize the action which contains all possible terms implied by the SW map. After renormalization we arrive at a different theory in which the relation between the coupling constants is changed. Thi…
Quantum motion equation and Poincare translation invariance of noncommutative field theory
研究了非对易标量场中真空态和非真空态之间的Moyal算符及其期望值。对于非对易$ϕ^{\star4}$标量场，我们从平移变换和拉格朗日场方程导出了它的能量动量张量。对于时空非对易的$θ^{0i}=0$，我们将海森堡和量子运动方程推广到非对易$ϕ^{\star4}$标量场的Moyal星积形式。然后我们证明了时空非对易$θ^{0i}=0$情形下非对易$ϕ^{\star4}$标量场的Poincar{\' e}平移不变性。
One Loop Renormalization of Spontaneously Broken U(2) Gauge Theory on Noncommutative Spacetime
研究了非对易时空中自发破缺的非阿贝尔规范理论的重整化问题。我们通过对U（2）情形的显式分析表明，紫外发散可以在一个圈能级上被去除，而所需的重整化常数与对易时空相同。因此，我们推动努力建设现实模型的规范相互作用的非对易时空。
The one-loop renormalization of the gauge sector in the θ-expanded noncommutative standard model
在本文中，我们构建了一个版本的标准模型规范扇区的非对易时空，这是一个单圈重整化的一阶展开中的非对易性参数$θ$。
Nowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on "noncommutative spaces" are indeed much investigated, and suffer from a new type of divergence called the ultraviolet-infrared mixing. However, this problem has recently been solved by H. Grosse and R. Wulkenhaar by adding to the action of a noncommutative scalar model a harmonic term, which renders it renormalizable. One aim of this thesis is the extension of this procedure to gauge theories on the Moyal space. Indeed, we have introduced…
Noncommutative QFT and Renormalization
形变空间上的场论受到IR/UV混合的影响，重整化一般被破坏。在与R。Wulkenhaar，我们中的一个人意识到了一种治愈这种疾病的方法，通过增加一个边缘算子。我们回顾这些想法，显示的应用程序$ϕ^3$模型和使用热核展开方法耦合到外部规范场的标量场理论上的$θ$变形空间，并获得非交换规范场的行动。
A nontrivial solvable noncommutative ϕ^3 model in 4 dimensions
我们通过将非对易自对偶模型映射到一个Kontsevich模型，研究了四维非对易自对偶模型的量子化。该模型被证明是renormalizable，提供一个额外的counterterterm相比，包括2维的情况下，可以被解释为分散的字段移位的。Kontsevich模型的已知结果允许获得自由能和任何n点函数的亏格展开，这对于重整化后的每个亏格都是有限的。不需要耦合常数或波函数重整化。确定了一个临界耦合，超过该临界耦合，模型是不稳定的。这提供了一个非平凡的相互作用NC场论在4维。
In this paper, we study the quantum behavior of the noncommutative Jackiw-Pi model. After establishing the Becchi-Rouet-Store-Tyutin (BRST) invariant action, the perturbative renormalizability is discussed, allowing us to introduce the renormalized mass and gauge coupling. We then proceed to compute the one-loop correction to the basic 1PI functions, necessary to determine the renormalized parameters (mass and charge), next we discuss the physical behaviour of these parameters.
Noncommutative renormalization for massless QED
本文从D.克莱默对于QED，我们描述了一个既不是交换的也不是余交换的重整化的Hopf代数。我们得到明确的重整化公式的电子和光子的传播，真空极化和电子的自能，这是相当于Zimmermann的森林公式的总和的所有费曼图在一个给定的相互作用顺序。然后，我们将由理论的耦合常数定义的Connes-Kreimer映射推广到QED，定义了一个非交换的非正规化Hopf代数，然后证明了电荷的重整化定义了这个Hopf代数与QED的重整化Hopf代数之间的同态。最后，我们表明，戴森公式的重整化的电子和光子传播可以给出一个非交换（如矩阵值）的形式。
5D Differential Calculus and Noether Analysis of Translation Symmetries in kappa-Minkowski Noncommutative Spacetime
我们进行了一个描述的平移变换在4D kappa-Minkowski非对易时空，这是基于一个5D微分结构的Noether分析。适当地考虑微分学的性质，我们得到了守恒电荷的一个显式公式。我们还提出了一个选择的基础上的5D演算，从而导致一个直观的描述时间导数。
We give here the Hopf algebra structure describing the noncommutative renormalization of a recently introduced translation-invariant model on Moyal space. We define Hochschild one-cocyles $B_+^γ$ which allows us to write down the combinatorial Dyson-Schwinger equations for noncommutative quantum field theory. One- and two-loops examples are explicitly worked out.
We study a self-interacting scalar $φ^4$ theory on the $d$-dimensional noncommutative torus. We determine, for the particular cases $d=2$ and $d=4$, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the UV/IR mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix $θ$.
Renormalization and Induced Gauge Action on a Noncommutative Space
形变空间上的场论受到IR/UV混合的影响，重整化一般被破坏。在与R。Wulkenhaar，我们中的一个人意识到了一种治疗这种疾病的方法，通过增加一个边缘算子。我们回顾这些想法，应用到$ϕ^3$模型，并使用热核展开方法耦合到一个外部规范场的标量场理论上的$θ$变形空间，并获得非对易规范行动。
Renormalization of the energy-momentum tensor in noncommutative scalar field theory
本文考虑四维复合算符的单圈重正化和非对易E4标量场理论中的能量动量张量。构造了适当的算子基，证明了裸复合算子可以用重整化算子表示，并借助于混合矩阵计算了其显式形式。相应的矩阵元素与交换理论不同。正则定义的能量动量张量不是有限的，必须用“改进的”张量来代替，以提供有限性。找到了合适的“改进”条件。
Heat Trace Asymptotics on Noncommutative Spaces
这是一个微型审查的热核展开的广义拉普拉斯在各种非交换空间。也被认为是光谱作用原理，重整化的非交换理论和异常的应用。
We compute the two-point and four-point Green's function of the noncommutative $ϕ^{4}$ field theory; first with the s-ordered star products and then with a general translation invariant star product. We derive the differential expression for any translation invariant star product, and with the help of this expression we show that any of these products can be written in terms of a twist. Finally, using the notion of the twisted action of the infinitesimal Poincaré transformations, we show that the commutator between the coordinate functions is invariant under Poincaré transformations at a defor…
We employ the path integral approach developed in [29] to discuss the (generalized) harmonic oscillator in a noncommutative plane. The action for this system is derived in the coherent state basis with additional degrees of freedom. From this the action in the coherent state basis without any additional degrees of freedom is obtained. This gives the ground state spectrum of the system. We then employ the exact renormalization group approach to show that an equivalence can be constructed between this (noncommutative) system and a commutative system.
In the previous study, we formulate a matrix model renormalization group based on the fuzzy spherical harmonics with which a notion of high/low energy can be attributed to matrix elements, and show that it exhibits locality and various similarity to the usual Wilsonian renormalization group of quantum field theory. In this work, we continue the renormalization group analysis of a matrix model with emphasis on nonlocal interactions where the fields on antipodal points are coupled. They are indeed generated in the renormalization group procedure and are tightly related to the noncommutative natu…
Propagators for Noncommutative Field Theories
在本文中，我们提供了精确的表达式，传播的非对易玻色子或费米场论后，添加条款的Grosse-Wulkenhaar型，以确保Langmann-Szabo协变性。我们强调新的费米的情况下，我们特别给出了所有必要的边界的多尺度分析和重整化的非对易Gross-Neveu模型。
Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
域壁孤立子是场论中最简单的拓扑对象。场论中的传统平移对称性是单参数畴壁解族的生成元，并诱导出沿畴壁传播的无质量模场。我们研究类似的问题，编织非交换场论具有Hopf代数平移对称性。作为一个具体的例子，我们讨论了李代数非对易时空中标量φ ^4编织非对易场论[x^i，x^j]= 2 i kappa <$^{ijk}x_k（i，j，k= 1，2，3）中具有Hopf代数平移对称性的畴壁孤子。首先利用Derrick定理讨论了畴壁孤子的存在性，并在非对易性参数kappa的扰动下构造了一个单参数解族.然后，我们找到了无质量模场，它在畴壁孤子上传播。我们进一步扩展我们的分析一般的Hopf代数平移对称。
On the 5D differential calculus and translation transformations in 4D kappa-Minkowski noncommutative spacetime
我们对四维$κ$ -Minkowski非对易时空中平移变换的描述进行了Noether分析，该分析基于一个五维微分的结构.我们中的一些人以前开发的技术（hep-th/0607221）描述的翻译转换的基础上的4D微分原来是适用的，没有任何修改，他们允许我们表明，通常采用的基础上的5D演算不考虑某些方面的结构的时间翻译在$κ$ -闵可夫斯基。我们提出了一个变化的基础上的5D演算，从而导致一个更直观的描述时间翻译。
Local Field Theory ON $κ$-Minkowski Space, Star Products and Noncommutative Translations
我们考虑局部场论上的$κ$ -变形Minkowski空间，这是一个例子，可解李代数非交换结构。利用$κ$ -Minkowski空间上的积分公式和$κ$ -变形傅里叶变换，我们考虑了变形局部场在标准Minkowski空间中的实性条件以及作用泛函的变形.给出了描述$κ$ -Minkowski空间上场论CBH量子化的两个等价星积的显式公式。利用星积技巧，我们还将$κ$ -Minkowski空间中的非对易平移表示为标准Minkowski空间中的对易平移.
A representation of general translation-invariant star products in the algebra of M(C) = lim_N\to \infty M_N (C) is introduced which results in the Moyal-Weyl-Wigner quantization. It provides a matrix model for general translation-invariant noncommutative quantum field theories in terms of the noncommutative calculus on differential graded algebras. Upon this machinery a cohomology theory, the so called star-cohomology, with groups H^k_*(C), is worked out which provides a cohomological framework to formulate general translation-invariant noncommutative quantum field theories based on the achie…
In this paper, we derive the energy momentum tensor for the translation invariant noncommutative Tanasa scalar field model. The Wilson regularization procedure is used to improve this tensor and the local conservation property is recovered. The same question is addressed in the case where the Moyal star product is deformed including the tetrad fields. It provides with an extension of the recent work [J. Phys. A: Math. Theor. 43 (2010) 155202], regarding the computation and properties of the Noether currents to the renormalizable models.
From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory
我们建立了伽罗瓦理论在其motivic形式与微扰重整化的数学理论（在最小减法方案与维数正则化）之间的精确关系。通过基于Birkhoff分解和t 'Hooft关系的Riemann-Hilbert对应，我们确定了一个包含重整化群并作用于物理理论集合的普适对称群（Cartier提出的“宇宙伽罗瓦群”）.这个群与动机伽罗瓦理论密切相关。我们构造了一个几何性质的普遍奇异框架，在这个框架中所有的发散都消失了。该文件包括一个详细的概述工作的康纳斯，Kreimer和背景材料的主要量子场论和代数几何概念。我们给出了一个完整的帐户，我们的结果宣布在数学。NT/0409306。
On Open String Sigma-Model and Noncommutative Gauge Fields
我们考虑开弦西格玛模型中的普通和非对易Dirac Born Infeld理论。首先，我们提出了一个重整化方案，混合点分裂正则化，直接导致Seiberg-Witten描述，包括他们的两种形式。我们还表明，这样的形式出现在标准重整化方案只是通过一些自由改变变量。其次，我们提出了一个在经典水平上具有非对易规范不变性的Wilson因子，然后在一个已知的保持非对易规范不变性的重整化方案中计算了西格玛模型的配分函数。结果，我们找到了非对易的Yang-Mills作用。
We investigate the effect of varying boundary conditions on the renormalization group flow in a recently developed noncommutative geometry model of particle physics and cosmology. We first show that there is a sensitive dependence on the initial conditions at unification, so that, varying a parameter even slightly can be shown to have drastic effects on the running of the model parameters. We compare the running in the case of the default and the maximal mixing conditions at unification. We then exhibit explicitly a particular choice of initial conditions at the unification scale, in the form …
Renormalization Group Invariant Constraints among Coupling Constants in a Noncommutative Geometry Model
研究了用非对易几何方法得到的标准模型的耦合常数之间的约束关系。首先，我们采用Álvarez等人的思想，分析了希格斯玻色子质量在重整化群下的演化。对于这一分析，我们通过修改Connes构造标准模型的方法，导出了两个确定的约束条件。其次，我们在NCG方法中找到了重整化群不变（RGI）约束。通过一个简单的例子，讨论了模型的耦合常数之间的约束成为RGI的条件与模型成为乘法可重正化的条件之间的关系。
Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map
我们证明了当使用Seiberg-Witten映射时，非对易$\mathbb{R}^4$上量子电动力学中的光子自能可以重整化到所有的阶数（在$θ$和$\hbar$中）.这是由于塞伯格-威滕映射具有极大的自由度，它代表了场的重新定义，并在$θ$变形的经典作用量中产生了所有那些规范不变项，这些项是补偿来自环路积分的发散所必需的。
A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogoliubov's recursion
Bogoliubov递推是微扰量子场论重整化过程中出现的一个特殊过程。它提供了收敛表达式，否则发散积分。我们在这里开发的非交换Rota-Baxter代数的功能标识的理论，这是编码，除其他外，这一过程中的背景下，康纳斯-Kreimer的霍普夫代数的重整化。我们的结果推广了交换Rota-Baxter代数的经典Spitzer型恒等式的Cartier-Rota理论。在经典的交换情形下，这些恒等式可以理解为从对称函数理论中导出。在这里，我们表明，一个类似的性质持有非交换Rota-Baxter代数。也就是说，我们表明，在非交换设置功能的身份可以从非交换对称函数的理论。李幂等元，特别是Dynkin幂等元在这个过程中起着至关重要的作用。他们的行动对亲幂幺群，如那些微扰重整化的详细描述的方式。
Renormalization of the energy-momentum tensor in noncommutative complex scalar field theory
研究了四维复合算符的重整化和非对易复标量场理论中的能量动量张量。定义了适当的算子基，并证明了裸复合算子可以通过一个在单圈近似下计算的混合矩阵的重整化算子来表示.基中算子的数目和形式以及混合矩阵的结构与相应的交换理论和非交换实标量场理论有本质的不同。我们证明了非对易复标量场理论中的能量动量张量可以定义为六个任意常数。正则定义的能量动量张量不是有限的，必须用“改进的”张量来代替，以提供有限性。找到了合适的“改进”项，并研究了零动量转移时四维复合算符的重整化。结果表明，混合矩阵是不同的情况下的任意和零动量转移。与能量动量张量不同的是，能量动量矢量的定义是明确的，不需要“改进”，至少在单圈近似下是守恒和有限的。
Some recent studies of the AdS/CFT correspondence for condensed matter systems involve the Fermi liquid theory as a boundary field theory. Adding B-flux to the boundary D-branes leads in a certain limit to the noncommutative Fermi liquid, which calls for a field theory description of its critical behavior. As a preliminary step to more general consideration, the modification of the Landau's Fermi liquid theory due to noncommutativity of spatial coordinates is studied in this paper. We carry out the renormalization of interactions at tree level and one loop in a weakly coupled fermion system in…
In this paper, we consider the $β$ function at one-loop approximation for noncommutative scalar QED. The renormalization of the full theory, including the basic vertices, and the renormalization group equation are fully established. Next, the complete set of the one-loop diagrams corresponding to the first-order radiative corrections to the basic functions is considered: gauge, charged scalar and ghost fields self-energies, and three- and four-point vertex functions $\left<ϕ^†ϕA\right>$ and $\left<ϕ^†ϕA A\right>$, respectively. We pay special attention to the noncommutative contributions to th…
Renormalization Group Equations and the Lifshitz Point In Noncommutative Landau-Ginsburg Theory
对任意维非对易Landau-Ginsburg理论进行了单圈重整化群（RG）分析.我们采用了现代版本的威尔逊RG方法，其中壳积分在动量空间绕过潜在的红外奇异性，由于紫外-红外混合。在RG变换下，相互作用顶点中的动量相关三角因子是边缘的，并且它们的边缘性在一个循环中保持不变，这是非交换几何的特征。一个负的$Θ$依赖的反常尺寸被发现作为一个新的效应的紫外-红外混合。我们还发现了一个非交换的Wilson-Fisher（NCWF）不动点在小于四维。在大的非对易性，量子涨落引起的动量空间不稳定性，并确定了相应的一阶相变连同在相图中的Lifshitz点。在Lifshitz点附近，我们引入了两个临界指数$ν_m$和$β_k$，它们的值在平均场水平上分别被确定为1/4和1/2。
Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars
非交换Feynman图是一个带状图，它可以画在亏格$g$ 2-曲面上.本文给出了非交换Feynman图在拓扑意义下的一般收敛定理，并对标量场中的几类图给出了证明。我们提出了Bogoliubov-Parasiuk的递归减法公式的一个非交换模拟，并证明了从一类$Ω_d$减去图满足收敛定理的条件。对于$\re^d$上的一般标量非对易量子场论，类$Ω_d$小于理论中所有图的类。这就留下了非对易场论的微扰重整化问题。我们评论了超对称性如何改善这种情况，并建议Wess-Zumino模型的非对易模拟是可重整化的。
One-loop renormalization of general noncommutative Yang-Mills field model coupled to scalar and spinor fields
研究了非对易U（N）Yang-Mills场与标量场和旋量场在基本表象和伴随表象下的相互作用理论。我们在作用量中既包括描述规范场和物质场之间相互作用的项，也包括仅描述物质场之间相互作用的项。其中有些相互作用项以前在非对易场论中没有考虑过。我们发现所有的理论是有限的在一个循环近似的抗衡。结果表明，这些反项可以通过场的重正化和耦合常数来吸收所有的发散，因此该理论是乘法重正化的。在1 PI规范场函数的情况下，结果可以很容易地推广到任意数量的物质场上。为了推广其他1 PI函数的结果，有必要以适当的方式调整物质耦合常数。在一些简单的情况下，这种推广的一部分，这些1 PI功能被认为是。
The ultraviolet/infrared (UV/IR) mixing of noncommutative field theories has been recently shown to be a generic feature of translation- invariant associative products. In this paper we propose to take into account the quantum corrections of the model to modify in this way the noncommutative action. This idea was already used to cure the UV/IR mixing for theories on Moyal space. We show that in the present framework also, this proposal proves successful for curing the mixing. We achieve this task by explicit calculations of one and higher loops Feynman amplitudes. For the sake of completeness,…
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