Volume 17, Issue 4, December 2010, Pages 485 - 490
The Quantization of a Fourth-Order Equation without a Second-Order Lagrangian
Authors
M. C. Nucci
Dipartimento di Matematica e Informatica, Università di Perugia, 06123 Perugia, Italy,nucci@unipg.it
P. G. L. Leach
School of Mathematical Sciences, Westville Campus, University of KwaZulu–Natal, Durban 4000, Republic of South Africa,leachp@nu.ac.za,leachp@math.aegean.gr
Received 22 August 2009, Accepted 23 April 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110001094How to use a DOI?
- Keywords
- Fourth-order ODE; Lagrangian; Lie symmetries; Hamiltonian; quantization
- Abstract
We present an equation of the fourth-order which does not possess a second-order Lagrangian and demonstrate by means of the method of reduction of order that one can obtain a first-order Lagrangian for it. This opens the way to quantization through the construction of an Hamiltonian which is suitable to be quantized according to the procedure of Dirac with the correct physical attributes.
- Copyright
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - M. C. Nucci AU - P. G. L. Leach PY - 2021 DA - 2021/01/07 TI - The Quantization of a Fourth-Order Equation without a Second-Order Lagrangian JO - Journal of Nonlinear Mathematical Physics SP - 485 EP - 490 VL - 17 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110001094 DO - 10.1142/S1402925110001094 ID - Nucci2021 ER -