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量子场论的可积性方法

Integrability methods in quantum field theory

  • 摘要: 可积量子场论是具有无穷多局域守恒流的特殊量子场论,一般只能定义在1+1维时空。这类量子场论可以用可积性方法精确求解,是研究非微扰量子场论的重要理论模型。近年来,可积性方法被应用于某些高维时空的量子场论的求解,对于深入理解高维量子场论和量子引力理论起到日益重要的作用。文章介绍可积量子场论的概念及精确求解的主要思想与方法。

     

    Abstract: An integrable quantum field theory is a special type of quantum field theory possessing infinitely many local conserved currents, which can generally only be defined in 1+1-dimensional spacetime. Such quantum field theories can be solved exactly using integrability methods and serve as an important prototype for studying non-perturbative quantum field theory. In recent years, integrability methods have been applied to solve certain quantum field theories in higher dimensional spacetimes, playing an increasingly significant role in deepening our understanding of higher-dimensional quantum field theories and quantum gravity. This article introduces the concept of integrable quantum field theories and the main ideas behind their exact solutions.

     

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