Dirac Lagrangian density : fractional formulation

Other Title(s)

كثافة لاغرانج ديراك : صياغة كسرية

Dissertant

al-Hejoj, Mayy Musa Mahmud

Thesis advisor

Hijjawi, Raid Shakir Abd al-Karim
Nawafleh, Khalid Isa

Comitee Members

al-Sharif, Abd al-Latif Mahmud
al-Gharayibah, Ismail Ahmad
Jawdah, Bassam rajab

University

Mutah University

Faculty

Faculty of Science

Department

Department of physics

University Country

Jordan

Degree

Master

Degree Date

2011

English Abstract

The main object of this work is to reformulate Dirac Lagrangian density by using Fractional Calculus method " Left–right Riemann- Liouville Fractional derivative". Using the fractional variational principle, we determine fractional Euler – Lagrange equations and fractional Hamiltonian equations resulting from the Dirac Lagrangian density using the same definition of the fractional derivatives. In the second part of this work we study the canonical quantization for the Dirac Lagragian density by defining the dynamical coordinates and the canonical conjugate momentum. Then we write the Hamiltonian in fractional form, also, we define the canonical commutation relations by the creation and innihilation operators. It is shown that the classical results are obtained as a particular case of the fractional formulation for both Euler–Lagrange and Hamilton equations.

Main Subjects

Mathematics

Topics

• Differential equations

No. of Pages

34

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-302192