Introduction to the Use of Non-Linear Techniques in S-Matrix Theory
I am going to explain to you how one can tackle certain problems in S-matrix theory that involve nonlinear functional equations. A physicist’s usual reaction to a non-linear equation of this kind would be either to try to get an approximate solution by iteration, or to introduce a linearization, perhaps in the neighbourhood of a known approximate solution. I will introduce some concepts of Banach space analysis , which will enable us to put these intuitive ideas on a rigorous basis. The advantage is that one can sometimes prove the existence of solutions of the exact equations, without any approximations.
KeywordsBanach Space Cauchy Sequence Contraction Mapping Contraction Mapping Principle Elastic Unitarity
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