Perturbation theory

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In mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In regular perturbation theory, the solution is expressed as a power series in a small parameter ε {\displaystyle \varepsilon } . The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of ε {\displaystyle \varepsilon } usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, often keeping only the first two terms: the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields and reaches its most sophisticated and advanced forms in quantum field theory...

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