BV形式主义中的渐近自由

Asymptotic symmetries in the BV-BFV formalism

We show how to derive asymptotic charges for field theories on manifolds with "asymptotic" boundary, using the BV-BFV formalism. We also prove that the conservation of said charges follows naturally from the vanishing of the BFV boundary action, and show how this construction generalises Noether's procedure. Using the BV-BFV viewpoint, we resolve the controversy present in the literature, regarding the status of large gauge transformation as symmetries of the asymptotic structure. We show that even though the symplectic structure at the asymptotic boundary is not preserved under these transfor…

Gauge Fixing and Constrained Dynamics

We review the Dirac formalism for dealing with constraints in a canonical Hamiltonian formulation and discuss gauge freedom and display constraints for gauge theories in a general context. We introduce the Dirac bracket and show that it provides a consistent method to remove any gauge freedom present. We discuss stability in evolution of gauge theories and show that fixing all gauge freedom is sufficient to ensure well-posedness for a large class of gauge theories. Electrodynamics provides examples of the methods outlined for general gauge theories. Future work will apply the formalism, and re…

二维O（3）模型中的拟渐近自由

Quasi-asymptotic freedom in the two dimensional O(3) model

数值研究了O（3）和十二面体自旋模型中重正化自旋2点函数的行为。Monte Carlo数据显示两个模型之间的良好协议。短距离行为非常接近标准的理论预期，但它与它有显着不同。这种情况提供了一个可能的解释。

一维相对论量子力学中$δ$ -函数势的渐近自由、维数变换和共形不动点

Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the $δ$-Function Potential in 1-dimensional Relativistic Quantum Mechanics

本文研究了一维$δ$函数势场中相对论性点粒子的薛定谔方程。使用维正则化，我们调查绑定和散射状态，我们得到的结果是一致的自伴扩展的伪微分算子$H = \sqrt{p^2 + m^2}$的抽象数学理论。有趣的是，这个相对简单的系统是渐近自由的。在无质量的极限，它经历了维度的嬗变，它拥有一个红外共形不动点。因此，它可以用来说明在相对论性量子力学的较简单的框架量子场论的非平凡的概念。

Asymptotic freedom for $λϕ^4_{\star}$ QFT in Snyder-de Sitter space

We analyze the model of a self-interacting $ϕ^4_{\star}$ scalar field theory in Snyder-de Sitter space. After analytically computing the one-loop beta functions {in the small noncommutativity and curvature limit}, we solve numerically the corresponding system of differential equations, showing that in this limit the model possesses at least one regime in which the theory is asymptotically free. Moreover, in a given region of the parameter space we also observe a peculiar running of the parameter associated to the curvature, which changes its sign and therefore can be interpreted as a transitio…

Conformal bridge between asymptotic freedom and confinement

We construct a nonunitary transformation that relates a given "asymptotically free" conformal quantum mechanical system $H_f$ with its confined, harmonically trapped version $H_c$. In our construction, Jordan states corresponding to the zero eigenvalue of $H_f$, as well as its eigenstates and Gaussian packets are mapped into the eigenstates, coherent states and squeezed states of $H_c$, respectively. The transformation is an automorphism of the conformal $\mathfrak{sl}(2,{\mathbb R})$ algebra of the nature of the fourth-order root of the identity transformation, to which a complex canonical tr…

一阶形式的渐近性和Hamilton性

Asymptotics and Hamiltonians in a First order formalism

我们考虑在空间无穷远渐近平坦的四维时空，并证明在一阶框架下广义相对论的作用量原理是明确的\emph{without the need of infinite counter terms.}。它自然地导致一个协变相空间，在这个协变相空间中，产生渐近对称的哈密顿量提供了时空的总能量动量和角动量。我们解决的微妙的，但重要的问题，因为在拉格朗日和哈密顿框架中的对数翻译和超翻译。正如一篇即将发表的论文所表明的，高维的处理要简单得多。我们的一阶框架也提出了一个新的方向推广的非交换几何的谱作用。

大$N$矩阵场论精确关联函数的渐近自由度

Seeing asymptotic freedom in an exact correlator of a large-$N$ matrix field theory

对于$(1+1)$维${\rm SU}(N)\times {\rm SU}(N)$主手征σ模型的大$N$（平面）极限，相关函数的精确表达式是已知的.这些都是用形状因子自举法，一个完全非微扰的方法。这个渐进自由模型的大- $N$解远不如O（$N$）sigma模型（或其他等矢量模型）的解那么微不足道。本文研究欧氏两点相关函数$N^{-1}< {\rm Tr}\,Φ(0)^{\dagger} Φ(x)>$，其中$Φ(x)\sim Z^{-1/2}U(x)$是标度场，$U(x)\in SU(N)$是裸场.我们用算子$\sqrt{-d^{2}/du^{2}}$的谱表示两点函数，其中$u\in (-1,1)$。在短距离下，这个表达式完全符合微扰重整化群的结果。