# Quantization of theories with non-Lagrangian equations of motion

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## Abstract

We present an approach to the canonical quantization of systems with non-Lagrangian equations of motion. We first construct an action principle for equivalent first-order equations of motion. Hamiltonization and canonical quantization of the constructed Lagrangian theory is a nontrivial problem, since this theory involves time-dependent constraints. We adapt the general approach to hamiltonization and canonical quantization for such theories (Gitman, Tyutin, 1990) to the case under consideration. There exists an ambiguity (not reduced to a total time derivative) in associating a Lagrange function with a given set of equations. We give a complete description of this ambiguity. It is remarkable that the quantization scheme developed in the case under consideration provides arguments in favor of fixing this ambiguity. Finally, as an example, we consider the canonical quantization of a general quadratic theory. Bibliography: 23 titles.

## Keywords

Poisson Bracket Action Principle Lagrange Function Hamiltonian Formulation Quantization Scheme## Preview

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