论文标题
正弦模型中的量子能不等式
A quantum energy inequality in the Sine--Gordon model
论文作者
论文摘要
我们考虑了该理论的有限制度$β^2 <4π$中无数正弦模型中的应力张量。我们证明了使用Bogoliubov公式在任意的Hadamard状态下定义的相互作用应力张量的重新归一化的扰动序列的收敛性，即使是因为涂抹仅沿着一维时时间般的世界线而不是在时空中。然后，我们表明，相互的能量密度，如遵循此世界线之后的观察者所见，它满足了绝对下限，这是一个独立于量子状态的界限。我们的证明采用和普遍的现有技术是由弗拉纳根，莱斯特和史密斯开发的。
We consider the stress tensor in the massless Sine--Gordon model in the finite regime $β^2 < 4 π$ of the theory. We prove convergence of the renormalised perturbative series for the interacting stress tensor defined using the Bogoliubov formula in an arbitrary Hadamard state, even for the case that the smearing is only along a one-dimensional time-like worldline and not in space-time. We then show that the interacting energy density, as seen by an observer following this worldline, satisfies an absolute lower bound, that is a bound independent of the quantum state. Our proof employs and generalises existing techniques developed for free theories by Flanagan, Fewster and Smith.
