Statistical field theory and matter under extreme conditions of temperature and density

统计场论是物理学家们非常感兴趣的。今天物理学中许多令人兴奋的问题只能用统计场论来研究。一个例子是夸克胶子等离子体，它可以在重离子的高能碰撞中形成。这样一种物质基本成分的等离子体可以教我们很多关于基本粒子相互作用的知识。另一个例子是对早期宇宙的研究，那里的物质和能量存在于高温下。 统计场论的研究在数学上是复杂的。其中一个主要的问题是，标准的近似技术，如微扰理论，不适用于其通常的形式。另一个问题是，大多数计算技术都假设系统已经达到平衡，这一假设对于我们想要研究的许多问题来说都是不合理的。场论的传统方法必须加以修改，以处理这类情况。

Statistical field theory is of great interest to physicists. Many exciting problems in physics today can only be studied using statistical field theory. One example is the quark gluon plasma which can be formed in a high energy collision of heavy ions. Such a plasma of the elementary constituents of matter can teach us a lot about fundamental particle interactions. Another example is the study of the early universe, where matter and energy exist at high temperatures. The study of statistical field theory is mathematically complex. One of the major problems is that standard approximation techniques, like perturbation theory, are not applicable in their usual forms. Another problem is that most calculation techniques assume that the system has reached equilibrium, an assumption that is not justified for many of the problems we want to study. The traditional techniques of field theory must be modified to handle situations of this type.