世界片上的场论：改进与推广
Field Theory On The World Sheet: Improvements And Generalizations
摘要：
本文是对平面φ ^3模型在不同维下的研究项目的继续。我们的想法是在世界片上重新表述它们，然后应用经典（平均场）近似，有两个目标：证明模型的基态是世界片上的孤子配置，孤子周围的量子涨落导致横向弦的形成。在回顾了一些早期的工作，我们介绍和讨论几个推广和新的结果。在1+2维空间中，建立了孤子能量的严格上限。添加了一个φ ^4相互作用以稳定原始的φ ^3模型。在1+3维和1+5维情况下，给出了一种改进的紫外发散处理方法。重要的是，我们证明了我们的近似方案可以嵌入到一个系统的强耦合展开。最后，孤立子周围的量子涨落谱证实了先前的结果：在1+2和1+3维中，世界片上形成了一个横向弦。
英文摘要：
This article is the continuation of a project of investigating planar phi^3 model in various dimensions. The idea is to reformulate them on the world sheet, and then to apply the classical (meanfield) approximation, with two goals: To show that the ground state of the model is a solitonic configuration on the world sheet, and the quantum fluctuations around the soliton lead to the formation of a transverse string. After a review of some of the earlier work, we introduce and discuss several generalizations and new results. In 1+2 dimensions, a rigorous upper bound on the solitonic energy is established. A phi^4 interaction is added to stabilize the original phi^3 model. In 1+3 and 1+5 dimensions, an improved treatment of the ultraviolet divergences is given. And significantly, we show that our approximation scheme can be imbedded into a systematic strong coupling expansion. Finally, the spectrum of quantum fluctuations around the soliton confirms earlier results: In 1+2 and 1+3 dimensions, a transverse string is formed on the world sheet.
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