An investigation of the Casimir energy for a fermion coupled to the sine-Gordon soliton with parity decomposition
We consider a fermion chirally coupled to a prescribed pseudoscalar field in the form of the soliton of the sine-Gordon model and calculate and investigate the Casimir energy and all of the relevant quantities, i.e. the spectrum of the states and the phase shifts, for each parity channel, separately...
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Published in | The European physical journal. C, Particles and fields Vol. 74; no. 8; pp. 1 - 11 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.08.2014
Springer |
Subjects | |
Online Access | Get full text |
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Summary: | We consider a fermion chirally coupled to a prescribed pseudoscalar field in the form of the soliton of the sine-Gordon model and calculate and investigate the Casimir energy and all of the relevant quantities, i.e. the spectrum of the states and the phase shifts, for each parity channel, separately. We present and use a simple prescription to construct the simultaneous eigenstates of the Hamiltonian and parity in the continua from the scattering states. We also use a prescription we had introduced earlier to calculate unique expressions for the phase shifts and check their consistency with both the weak and the strong forms of the Levinson theorem. In the graphs of the total and parity decomposed Casimir energies as a function of the parameters of the pseudoscalar field distinctive deformations appear whenever a fermionic bound state energy level with definite parity crosses the line of zero energy. However, the latter graphs show considerable sensitivity to the fine details of the shape of the background field which cannot be seen from the graph of the total Casimir energy. Finally, we consider a system consisting of a valence fermion in the ground state and find that the most energetically favorable configuration is the one with a soliton of winding number one, and this conclusion does not hold for each parity, separately. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 1434-6044 1434-6052 |
DOI: | 10.1140/epjc/s10052-014-3020-2 |