Quantizing non-Lagrangian gauge theories: an augmentation method

We discuss a recently proposed method of quantizing general non-Lagrangiangauge theories. The method can be implemented in many different ways, inparticular, it can employ a conversion procedure that turns an originalnon-Lagrangian field theory in $d$ dimensions into an equivalent Lagrangiantopological field theory in $d+1$ dimensions. The method involves, besides theclassical equations of motion, one more geometric ingredient called theLagrange anchor. Different Lagrange anchors result in different quantizationsof one and the same classical theory. Given the classical equations of motionand Lagrange anchor as input data, a new procedure, called the augmentation, isproposed to quantize non-Lagrangian dynamics. Within the augmentationprocedure, the originally non-Lagrangian theory is absorbed by a widerLagrangian theory on the same space-time manifold. The augmented theory is notgenerally equivalent to the original one as it has more physical degrees offreedom than the original theory. However, the extra degrees of freedom arefactorized out in a certain regular way both at classical and quantum levels.The general techniques are exemplified by quantizing two non-Lagrangian modelsof physical interest.Comment: 46 pages, minor correction