Resummation

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

• Perturbation theory
• Perturbation theory (quantum mechanics)

References

1. Feynman R.P., Kleinert H. (1986). "Effective classical partition functions" (PDF). Physical Review A. 34 (6): 5080–5084. Bibcode:1986PhRvA..34.5080F. doi:10.1103/PhysRevA.34.5080. PMID   9897894. Archived from the original (PDF) on 2020-03-12. Retrieved 2013-06-25.
2. Janke W., Kleinert H. (1995). "Convergent Strong-Coupling Expansions from Divergent Weak-Coupling Perturbation Theory" (PDF). Physical Review Letters . 75 (6): 2787–2791. arXiv: quant-ph/9502019 . Bibcode:1995PhRvL..75.2787J. doi:10.1103/physrevlett.75.2787. PMID   10059405. S2CID   119510120.
3. 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

• Hagen Kleinert and V. Schulte-Frohlinde (2001), Critical Properties of φ⁴-Theories, Singapore: World Scientific, ISBN   981-02-4658-7 (paperback), especially chapters 16-20.