Quantizing non-Lagrangian gauge theories: an augmentation method

TL;DR

This paper introduces an augmentation method for quantizing non-Lagrangian gauge theories by embedding them into a larger Lagrangian framework, utilizing the Lagrange anchor to handle different quantizations.

Contribution

It proposes a novel augmentation procedure that quantizes non-Lagrangian dynamics by embedding them into an extended Lagrangian theory, accommodating different Lagrange anchors.

Findings

The augmentation method successfully quantizes non-Lagrangian models.

Extra degrees of freedom are systematically factorized out.

The approach is exemplified on two physically relevant models.

Abstract

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.