Hamiltonian Formulation of Generalized Classical Field Systems Using Linear fields variables (𝝓, 𝑨𝒊, 𝑨𝒋)

Authors

Y. M. Alawaideh, MEU Research Unit, Middle East University, Amman, JordanFollow
B. M. Alkhamiseh, MEU Research Unit, Middle East University, Amman, JordanFollow
S. E. Alawideh, Department of Chemistry, Isra University, Amman, JordanFollow
D. Baleanu, Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey\\ Institute of Space Sciences, Magurele, 077125 Bucharest, RomaniaFollow
B. Abu-Izneid, Department of Electrical Engineering, University of Business and Technology, Jeddah 21432, Saudi ArabiaFollow
Jihad Asad, Dep. of Physics, Faculty of Applied science, Palestine Technical University -Kadoorie Tulkarm P 305, PalestineFollow

Author Country (or Countries)

Jordan

Abstract

The functional variational principle and differential equations of motion for the Lee–Wick electrodynamics equation are investigated in this study. A functional Hamiltonian principle is built utilizing the concept of a functional derivative. The Hamiltonian formulation of third-order continuous field systems is created using functional derivatives for continuous third-order systems. The formalism is generalized, and this new formulation is used to solve the Lee–Wick electrodynamics equation. We used the Euler-Lagrange equations for these systems to compare the results obtained using Hamiltons equations in terms of functional derivatives. To compare the outcomes of the two methodologies in terms of functional derivatives, one example has been presented. The results of this study show that functional calculus has more flexible models than classical calculus due to the ordering of the functional derivative and the functional operator. This property is critical when developing a novel generalization of the Lee-Wick equation using functional derivatives.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/jsap/120215

Recommended Citation

M. Alawaideh, Y.; M. Alkhamiseh, B.; E. Alawideh, S.; Baleanu, D.; Abu-Izneid, B.; and Asad, Jihad (2023) "Hamiltonian Formulation of Generalized Classical Field Systems Using Linear fields variables (𝝓, 𝑨𝒊, 𝑨𝒋)," Journal of Statistics Applications & Probability: Vol. 12: Iss. 2, Article 16.
DOI: http://dx.doi.org/10.18576/jsap/120215
Available at: https://digitalcommons.aaru.edu.jo/jsap/vol12/iss2/16