An Introduction to String Field Theory
An Introduction to String Field Theory
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弦场论简介
DOI：
10.1111/j.1749-6632.1987.tb40382.x
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
G. West
中科院分区：
文献类型：
--
作者：
G. West
基本粒子相互作用的场论公式最吸引人的一个方面是，它非常自然地结合了一般的对称性，如洛伦兹和规范不变性。此外，由自发对称性破缺或理论的底层拓扑结构引起的非扰动效应最容易容纳在这个框架内。事实上，标准模型的通常表述和理解在场论之外几乎是不可想象的。因此，尝试类似的弦理论公式是很自然的，因为随着最近异常抵消的发现，“这些已经成为对包括引力在内的所有相互作用的完全统一描述的严肃候选者。”在弦的情况下，可能有更强的动机来进行规范不变的场论描述，因为它的一个更显著的特性是无质量规范粒子（特别是引力子）的自动出现，而不需要明确引入一些类似于爱因斯坦一般坐标不变性或等效原理的基本原理。据推测，这个谜团的一部分是由于这些理论是在物理光锥规范中制定的，从而掩盖了任何一般的潜在规范对称性。对于相互作用的弦，一个完全规范不变作用的公式有望使我们更深入地理解这些理论是如何以及为什么起作用的，并最终了解其基本原理到底是什么。此外，如果没有这样的表述，似乎不可能动态地理解四维“真实”世界的紧化问题，因为这需要理解理论的真空结构。普通场论基于牛顿的点粒子概念，其运动由一维世界线x ~ (T)描述，由演化参数（时间）T参数化（见图1）。原则上，我们可以根据这些第一个量子化的世界线来建立粒子相互作用，而不需要明确引用一个场，从而计算所有的s矩阵元素。通常情况下，人们不会这么做；取而代之的是引入一个局部场4(x)它的傅里叶分量表示给定动量的粒子的产生或毁灭。在这种形式中，粒子的散射归因于不同场之间的局部相互作用。作为世界线和场之间对偶性的最简单的例子，我将（在下面）检查一个自由相对论性点粒子的情况，并说明如何
One of the most appealing aspects of the field theoretic formulation of elementary particle interactions is that it very naturally incorporates general symmetry properties such as Lorentz and gauge invariance. Furthermore, nonperturbative effects arising from spontaneous symmetry breaking or from the underlying topological structure of the theory are most easily accommodated within this framework. Indeed, the usual formulation and understanding of the standard model is almost unthinkable outside of field theory. Therefore, it is quite natural to attempt a similar formulation for string theories because with the recent discovery of anomaly cancellations,' these have emerged as serious candidates for a completely unified description of all the interactions including gravitation.' In the string case, there is perhaps even stronger motivation for a gauge-invariant field theoretic description because one of its more remarkable properties is the automatic appearance of massless gauge particles (in particular, the graviton) without the explicit introduction of some fundamental principle akin to Einstein's general coordinate invariance or the principle of equivalence. Presumably, part of this mystery is due to the fact that these theories were formulated in the physical light-cone gauge, thereby masking any general underlying gauge symmetry. The formulation of a completely gauge-invariant action for the interacting string would hopefully lead to a deeper understanding of how and why these theories work and, ultimately, what the underlying principle actually is. Furthermore, without such a formulation, it would seem unlikely that the question of compactification to a four-dimensional "real" world could be dynamically understood because this requires an understanding of the vacuum structure of the theory. Ordinary field theory is based upon the Newtonian concept of point particles whose motion is described by one-dimensional world lines, x ~ ( T ) , parametrized by the evolution parameter (time) T (see FIGURE 1). In principle, one could set up particle interactions in terms of these first quantized world lines without explicit reference to a field and thereby calculate all S-matrix elements. Typically, this is not what is done; instead, one introduces a local field 4(x) whose Fourier components represent the creation or destruction of particles of a given momentum. In this formalism, the scattering of particles is ascribed to local interactions among the various fields. As the simplest possible example of this duality between a world-line and field formulation, I shall examine (below) the case of a free relativistic point particle and show how the