Quantization of theories with non-Lagrangian equations of motion
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Tome 331 (2006), pp. 30-42
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We present an approach to the canonical quantization of systems with
non-Lagrangian equations of motion. We first construct an action principle
for an equivalent first-order equations of motion. A hamiltonization and
canonical quantization of the constructed Lagrangian theory is a non-trivial
problem, since this theory involves time-dependent constraints. We adopt the
general approach of 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 the 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.
@article{ZNSL_2006_331_a3,
author = {D. M. Gitman and V. G. Kupriyanov},
title = {Quantization of theories with {non-Lagrangian} equations of motion},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {30--42},
publisher = {mathdoc},
volume = {331},
year = {2006},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_331_a3/}
}
D. M. Gitman; V. G. Kupriyanov. Quantization of theories with non-Lagrangian equations of motion. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Tome 331 (2006), pp. 30-42. http://geodesic.mathdoc.fr/item/ZNSL_2006_331_a3/