Dirac Lagrangian Density
- Details
- Category: Physics
- Published: Tuesday, 01 May 2012 03:00
- Written by Mai Mousa Al-Hejoj
- Hits: 3373
Abstract
Dirac lagranglan density "fractional formulation"
Mai Mousa Al-Hejoj
Mu'tah University, 2011
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.