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 experi ...
, 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 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
Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superflu ...
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 chemistry, q ...
it was extended to any order here, and in
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles a ...
here.
[
Kleinert, H.]
"Critical exponents from seven-loop strong-coupling φ4 theory in three dimensions"
Physical Review
''Physical Review'' is a peer-reviewed scientific journal established in 1893 by Edward Nichols. It publishes original research as well as scientific and literature reviews on all aspects of physics. It is published by the American Physical Soc ...
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)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for whi ...
References
Books
*
Hagen Kleinert, ''Critical Properties of φ
4-Theories''
World Scientific (Singapore, 2001) Paperback '' (also availabl
online (together with V. Schulte-Frohlinde).''
Quantum field theory
Summability methods
{{quantum-stub