Variational perturbation theory

Variational perturbation theory

In mathematics, variational perturbation theory is a mathematical method to convert divergent power series in a small expansion parameter, say

:s=sum_{n=0}^infty a_n g^n,

into a convergent series in powers

:s=sum_{n=0}^infty b_n /(g^omega)^n,

where omega is a critical exponent. This is possible with the help of variational parameters, which are determined by optimization order by order in g.

Variational perturbation theory is an important mathematical tool in the theory of critical phenomena. It has led to the most accurate predictions of critical exponents.

See also

* Variational method (quantum mechanics)

References

* Hagen Kleinert, "Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets", 3. Auflage, [http://www.worldscibooks.com/physics/5057.html World Scientific (Singapore, 2004)] (readable online [http://www.physik.fu-berlin.de/~kleinert/b5 here] )" (see Chapter 15)
* Hagen Kleinert and Verena Schulte-Frohlinde, "Critical Properties of φ4-Theories", [http://www.worldscibooks.com/physics/4733.html World Scientific (Singapur, 2001)] ; Paperback ISBN 981-02-4658-7 "(readable online [http://www.physik.fu-berlin.de/~kleinert/b8 here] )" (see Chapter 19)


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