标题： 字符串量化：福克与LQG表示 显示英文标题

标题： String quantization: Fock vs. LQG Representations

摘要： 我们建立了一个统一的框架，以比较两种方法中玻色弦的量子化：一种是由Thiemann提出的，基于环量子引力的方法；另一种是使用通常的福克空间量子化方法。 两者都得出一个微分同胚不变的量子理论。 我们讨论了为什么Thiemann的方法中没有中心电荷，但具有环方法在微分同胚不变理论中的不连续性特征。 然后我们通过谐振子的例子说明这种不连续性的(非)物理后果，例如能量谱无界。 另一方面，在连续的福克表示中，必须使用Gupta和Bleuler的方法来构造微分同胚的幺正算符，该方法将微分同胚群表示到一个由通常中心电荷给出的相位。 显示英文摘要

摘要： We set up a unified framework to compare the quantization of the bosonic string in two approaches: One proposed by Thiemann, based on methods of loop quantum gravity, and the other using the usual Fock space quantization. Both yield a diffeomorphism invariant quantum theory. We discuss why there is no central charge in Thiemann's approach but a discontinuity characteristic for the loop approach to diffeomorphism invariant theories. Then we show the (un)physical consequences of this discontinuity in the example of the harmonic oscillators such as an unbounded energy spectrum. On the other hand, in the continuous Fock representation, the unitary operators for the diffeomorphisms have to be constructed using the method of Gupta and Bleuler representing the diffeomorphism group up to a phase given by the usual central charge.