1212.2089 (Siamak S. Gousheh et al.)

Casimir Energy for a Fermion Coupled to the Sine-Gordon Model    [PDF]

Siamak S. Gousheh, Azadeh Mohammadi, Leila Shahkarami

We compute the Casimir energy for a fermion chirally coupled to a prescribed pseudoscalar field in the form of the soliton of the sine-Gordon model. The classical equations of this system are not analytically solvable. We obtain the bound energies of the Fermi field using a numerical method called the relaxation method, and its continuum scattering wavefunctions by the use of the Runge-Kutta-Fehlberg of order 6. Then, we obtain a linear combination of the obtained scattering states, which is the simultaneous eigenstate of the Hamiltonian and parity. Using the obtained scattering wavefunctions and the parity eigenstates, we are able to calculate both the scattering phase shifts and the phase shifts of the parity ones. The resulting phase shifts are consistent with both the weak and strong forms of the Levinson theorem. Having these phase shifts we can compute the Casimir energy of the system in two different ways. We can use the scattering phase shifts to obtain the Casimir energy, or equivalently add the Casimir energy for each parity, calculated by the phase shift for the corresponding parity...

View original: http://arxiv.org/abs/1212.2089