UNDERSTANDING SOLITONS ALGEBRAICALLY

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Abstract
We describe techniques we have developed to analyze the physics of topological solitons in a model-independent way. Our central result is to show that topological solitons in generic field theories exhibit Bogomol’nyi bounds and Bogomol’nyi equations. Our methods turn the derivation of these Bogomol’nyi relationships into algebraic calculations and do not depend on the particular equations of motion. We present a discussion of the O(3) nonlinear σ-model as an example of our techniques.

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