Resummation
Jump to navigation
Jump to search
In mathematics and theoretical physics, 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 rescaled, 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 and H. Kleinert.[1] Feynman and Kleinert's technique has been extended to arbitrary order in quantum mechanics[2] and quantum field theory.[3]
See also
[edit | edit source]References
[edit | edit source]- ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- ^ Kleinert, H., "Critical exponents from seven-loop strong-coupling φ4 theory in three dimensions" Archived 2020-03-12 at the Wayback Machine. Physical Review D 60, 085001 (1999)
Books
[edit | edit source]- Hagen Kleinert and V. Schulte-Frohlinde (2001), Critical Properties of φ4-Theories, Singapore: World Scientific, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value). (paperback), especially chapters 16-20.
