We discuss a recently proposed method of quantizing general non-Lagrangian gauge theories. The method can be implemented in many different ways, in particular, it can employ a conversion procedure that turns an original non-Lagrangian field theory in $d$ dimensions into an equivalent Lagrangian topological field theory in $d+1$ dimensions. The method involves, besides the classical equations of motion, one more geometric ingredient called the Lagrange anchor. Different Lagrange anchors result in different quantizations of one and the same classical theory. Given the classical equations of motion and Lagrange anchor as input data, a new procedure, called the augmentation, is proposed to quantize non-Lagrangian dynamics. Within the augmentation procedure, the originally non-Lagrangian theory is absorbed by a wider Lagrangian theory on the same space-time manifold. The augmented theory is not generally equivalent to the original one as it has more physical degrees of freedom than the original theory. However, the extra degrees of freedom are factorized out in a certain regular way both at classical and quantum levels. The general techniques are exemplified by quantizing two non-Lagrangian models of physical interest.
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机译:我们讨论了最近提出的量化一般非拉格朗日规理论的方法。该方法可以以许多不同的方式实现,特别是,它可以采用将$ d $维的原始非拉格朗日场理论转换为$ d + 1 $维的等效拉格朗日拓扑场论的转换程序。除了经典的运动方程式之外,该方法还涉及一种称为拉格朗日锚的几何元素。不同的拉格朗日锚会导致对一个和同一经典理论的不同量化。给定经典的运动方程和拉格朗日锚作为输入数据,提出了一种称为增广的新程序来量化非拉格朗日动力学。在扩充过程中,最初的非拉格朗日理论被同一时空流形上的更宽的拉格朗日理论所吸收。增强理论通常不等同于原始理论,因为它比原始理论具有更大的物理自由度。但是,额外的自由度在古典和量子级别都以一定的规则方式被分解。通过量化两个物理兴趣的非拉格朗日模型来举例说明一般技术。
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