论文标题
非线性Sigma模型的Casimir效应和Mermin-Wagner-Hohenberg-Coleman定理
The Casimir effect for nonlinear sigma models and the Mermin-Wagner-Hohenberg-Coleman theorem
论文作者
论文摘要
已知由非相互作用的无质量量子引起的量子真空（Casimir）能量会诱导远距离力，而对于大量田间和分离的衰减比所涉及的量子的逆质量大。在这里，我们表明，维度和非线性之间的相互作用以非平凡的方式改变了这种行为。我们认为，这些变化与Mermin-Wagner-Hohenberg-Coleman定理密切相关，并使用非线性Sigma模型作为工作示例来说明这种情况。我们计算了量子真空能，该量子真空能由通常的casimir贡献和半经典的贡献组成，并发现真空诱导的力在较大距离处长度远，而在小分离处则表现出复杂的行为。最后，即使对于这种相对简单的设置，我们也表明非线性通常负责该力中的调制作为耦合常数和温度的函数。
The quantum vacuum (Casimir) energy arising from noninteracting massless quanta is known to induce a long-range force, while decays exponentially for massive fields and separations larger than the inverse mass of the quanta involved. Here, we show that the interplay between dimensionality and nonlinearities in the field theory alters this behaviour in a nontrivial way. We argue that the changes are intimately related to the Mermin-Wagner-Hohenberg-Coleman theorem, and illustrate this situation using a nonlinear sigma model as a working example. We compute the quantum vacuum energy, which consists of the usual Casimir contribution plus a semiclassical contribution, and find that the vacuum-induced force is long-ranged at large distance, while displays a complex behaviour at small separations. Finally, even for this relatively simple set-up, we show that nonlinearities are generally responsible for modulations in the force as a function of the coupling constant and the temperature.
