软同步规范：主值处方
Soft synchronous gauge: principal value prescription
AI总结：
本文提出用主值处方处理同步规范中引力子传播子的奇异性，通过引入规范破坏项构造传播子，并证明鬼场贡献在极限下可忽略。
摘要：
引力中的同步规范（$g_{0 λ} = - δ_{0 λ}$）由于引力子传播子中 $p_0 = 0$ 处的奇异性而定义不明确。此前我们研究了通过考虑规范 $n^λg_{λμ} = 0$，$n^λ= (1, - \varepsilon (\partial^j \partial_j )^{- 1} \partial^k )$ 并在 $\varepsilon \to 0$ 极限下对该规范进行“软化”。现在我们探索使用主值处方（不是标准柯西意义上的）的可能性，粗略地说，这相当于将奇异性 $p_0^{-j}$ 替换为 $[ (p_0 + i \varepsilon )^{-j} + (p_0 - i \varepsilon )^{-j} ] / 2$，从而使其表现得像分布。我们证明，这样的传播子是在作用量中加入一个一般形式的规范破坏项后得到的，该项约化为 $\sim \int f_λΛ^{λμ} f_μ\d^4 x$，其中 $Λ^{λμ}$ 是一个依赖于 $\partial$ 的常数算符，$f_λ$ 是一个度规泛函。分析了鬼场对有效作用量的贡献。对于所需的中间正则化，暗示了理论在小距离处的离散结构。结果表明，在 $\varepsilon \to 0$ 极限下，鬼场贡献可以忽略不计。
英文摘要：
The synchronous gauge in gravity ($g_{0 λ} = - δ_{0 λ}$) is ill-defined due to the singularity at $p_0 = 0$ in the graviton propagator. Previously we studied "softening" this gauge by considering instead the gauge $n^λg_{λμ} = 0$, $n^λ= (1, - \varepsilon (\partial^j \partial_j )^{- 1} \partial^k ) $ in the limit $\varepsilon \to 0$. We now explore the possibility of using a principal value prescription (not in the standard Cauchy sense), which amounts, roughly speaking, to replacing singularities $p_0^{-j} \Rightarrow [ (p_0 + i \varepsilon )^{-j} + (p_0 - i \varepsilon )^{-j} ] / 2$, which then behave like distributions. We show that such a propagator follows upon adding to the action a gauge-violating term of a general form, which reduces to $ \sim \int f_λΛ^{λμ} f_μ\d^4 x $ with a constant operator $Λ^{λμ}$ depending on $\partial$ and a metric functional $f_λ$. The contribution of the ghost fields to the effective action is analysed. For the required intermediate regularization, the discrete structure of the theory at small distances is implied. It is shown that the ghost contribution can be disregarded in the limit $ \varepsilon \to 0$.
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