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derrick's theorem

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24 - Derrick’s Theorem, Bogomolnyi Bound, theAbelian-Higgs System, andSymmetryBreaking
from Part II - Solitons and Topology; Non-Abelian Theory
Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
Book:

Classical Field Theory

Published online:

04 March 2019

Print publication:

14 March 2019, pp 217-225
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Summary

We prove Derrick's theorem about scalar field solitons, then we derive the Bogomolnyi bound for the energy of scalar field configurations in 1+1 dimensions and consider the example of the Higgs system and its kink soliton. Then we consider spontaneous symmetry breaking in the Abelian–Higgs syste, and the different fluctuations and their masses, as well as the description of this system in an unitary gauge. We end with a quick treatment of the non-Abelian Higgs system.