畴壁非线性量子化
Domain wall nonlinear quantization
摘要：
考虑畴壁（余维为1的相对论膜）的非线性量子化。膜尘方程被认为是Hamilton-Jacobi方程的一个类似物，这使我们能够构造它的量子类似物。所得方程具有非线性Klein-Fock-Gordon方程的形式。它可以解释为量子畴壁的平均场近似。色散关系获得小扰动（线性近似）。扰动的群速度不超过光速。对于沿畴壁传播的微扰，除了无质量模（如经典情况）外，还会出现大质量模。这个结果在凝聚态理论和超弦与超引力理论中的膜量子化中可能是有趣的。
英文摘要：
The nonlinear quantization of the domain wall (relativistic membrane of codimension 1) is considered. The membrane dust equation is considered as an analogue of the Hamilton-Jacobi equation, which allows us to construct its quantum analogue. The resulting equation has the form of a nonlinear Klein-Fock-Gordon equation. It can be interpreted as the mean field approximation for a quantum domain wall. Dispersion relations are obtained for small perturbations (in a linear approximation). The group speed of perturbations does not exceed the speed of light. For perturbations propagating along the domain wall, in addition to the massless mode (as in the classical case), a massive one appears. The result may be interesting in condensed matter theory and in membrane quantization in superstring and supergravity theories.
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