A summary on Solitons in Quantum field theory
This text is a brief summary on solitons in quantum field theory. An introduction to quantum field theory is made through which certain notions in the theory of solitons in quantum field theory is possible to understand. The explicit time-independent kink solutions are computed for the phi^4- and the sine-Gordon theory. The time-dependent kink solutions were then found by Lorentz transformation of the time- independent solutions. Interesting quantities such as the kink mass, the charge and the energy density is computed in both phi^4- and the sine-Gordon theory. An investigation of geometrical methods for finding the integrals of motions for the sine-Gordon field is made. Additionally the equivalence between the sine- Gordon model and the massive Thirring model is presented.
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