论文标题
正弦模型中的本地操作员：$ \partial_μx\，\ partial_νϕ $和压力张量
Local operators in the Sine-Gordon model: $\partial_μϕ\, \partial_νϕ$ and the stress tensor
论文作者
论文摘要
我们考虑了无数正弦模型中最简单的非平凡的本地复合算子，该模型是$ \ partial_μϕ \，\ partial_νϕ $和应力张量$ t_ {μν} $。我们表明，即使在该理论的有限状态$β^2 <4π$中，这些运算符也需要在扰动理论中的每个顺序上进行额外的重量量量标尺（超出自由场正常订购）。我们进一步证明了在Euclidean签名和Minkowski时空的期望值中，重新归一化的扰动序列的收敛性，以及在任意Hadamard状态下的后者。最后，我们表明必须向重量化的应力张量添加量子校正（与$ \ hbar $成比例）以获得保守数量。
We consider the simplest non-trivial local composite operators in the massless Sine-Gordon model, which are $\partial_μϕ\, \partial_νϕ$ and the stress tensor $T_{μν}$. We show that even in the finite regime $β^2 < 4 π$ of the theory, these operators need additional renormalisation (beyond the free-field normal-ordering) at each order in perturbation theory. We further prove convergence of the renormalised perturbative series for their expectation values, both in the Euclidean signature and in Minkowski space-time, and for the latter in an arbitrary Hadamard state. Lastly, we show that one must add a quantum correction (proportional to $\hbar$) to the renormalised stress tensor to obtain a conserved quantity.
