In
mathematics and
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
, resummation is a procedure to obtain a finite result from a
divergent sum (series) of
functions. Resummation involves a definition of another (convergent) function in which the individual terms defining the original function are re-scaled, and an integral transformation of this new function to obtain the original function.
Borel resummation
In mathematics, Borel summation is a summation method for divergent series, introduced by . It is particularly useful for summing divergent asymptotic series, and in some sense gives the best possible sum for such series. There are several va ...
is probably the most well-known example.
The simplest method is an extension of a variational approach to higher order based on a paper by
R.P. Feynman and
H. Kleinert.
In
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...
it was extended to any order here, and in
quantum field theory here.
[
Kleinert, H.]
"Critical exponents from seven-loop strong-coupling φ4 theory in three dimensions"
Physical Review D 60, 085001 (1999)
See also Chapters 16–20 in the textbook cited below.
See also
*
Perturbation theory
In mathematics and applied 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 middl ...
*
Perturbation theory (quantum mechanics)
References
Books
*
Hagen Kleinert
Hagen Kleinert (born 15 June 1941) is professor of theoretical physics at the Free University of Berlin, Germany (since 1968)Honorary Doctorat the
West University of Timișoaraandat thin Bishkek. He is alsHonorary Memberof th For his contributio ...
, ''Critical Properties of φ
4-Theories''
World Scientific (Singapore, 2001) Paperback '' (also availabl
online (together with V. Schulte-Frohlinde).''
Quantum field theory
Summability methods
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