Local covariance and background independence

Locally covariant charged fields and background independence

We discuss gauge background independence at the example of the charged Dirac field. We show that a perturbative version of background independence, termed perturbative agreement by Hollands and Wald, can be fulfilled, and discuss some of its consequences.

Background independence in gauge theories

Classical field theory is insensitive to the split of the field into a background configuration and a dynamical perturbation. In gauge theories, the situation is complicated by the fact that a covariant (w.r.t. the background field) gauge fixing breaks this split independence of the action. Nevertheless, background independence is preserved on the observables, as defined via the BRST formalism, since the violation term is BRST exact. In quantized gauge theories, however, BRST exactness of the violation term is not sufficient to guarantee background independence, due to potential anomalies. We …

背景无关性与Adler-Bardeen定理

Background independence and the Adler-Bardeen theorem

该研究通过将规范反常与形式化背景无关性的微扰一致性关联，证明含任意紧致规范群及物质耦合的可重整Yang-Mills规范理论的规范反常不存在性可在单圈水平确立。

正则量子引力中背景独立性的一些令人惊讶的含义

Some surprising implications of background independence in canonical quantum gravity

有一种精确的意义，即背景独立性的要求足以唯一地选择圈量子引力（LQG）的运动学。具体地说，LQG的基本运动代数承认一个唯一的同构不变状态。虽然这个结果已经被严格地建立起来，但对于研究量子引力的其他方法的研究人员来说，这是一个惊喜。这篇文章的目的是用几何动力学的教学方式来解释根本原因，保持最低限度的技术性。这一讨论将揭示出非微扰、正则量子引力中的量子态不变性（和协变性）所起的惊人的强大作用。

The microlocal spectrum condition, initial value formulations and background independence

We analyze the implications of the microlocal spectrum/Hadamard condition for states in a (linear) quantum field theory on a globally hyperbolic spacetime $M$ in the context of a (distributional) initial value formulation. More specifically, we work in a $3+1$-split $M\cong\mathbb{R}\timesΣ$ and give a bound, independent of the spacetime metric, on the wave front sets of the initial data for a quasi-free Hadamard state in the quantum field theory defined by a normally hyperbolic differential operator $P$ acting in a vector bundle $E\stackrelπ{\rightarrow}M$. This aims at a possible way to appl…

Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence

We compute non-extremal three-point functions of scalar operators in $\mathcal{N}=4$ super Yang-Mills at tree-level in $g_{YM}$ and at finite $N_c$, using the operator basis of the restricted Schur characters. We make use of the diagrammatic methods called quiver calculus to simplify the three-point functions. The results involve an invariant product of the generalized Racah-Wigner tensors ($6j$ symbols). Assuming that the invariant product is written by the Littlewood-Richardson coefficients, we show that the non-extremal three-point functions satisfy the large $N_c$ background independence; …