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 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 and H. Kleinert. In quantum mechanics it was extended to any order here, and in quantum field theory here. See also Chapters 16–20 in the textbook cited below.
- 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.
- Janke W., Kleinert H. (1995). "Convergent Strong-Coupling Expansions from Divergent Weak-Coupling Perturbation Theory" (PDF). Physical Review Letters. 75 (6): 287. arXiv:quant-ph/9502019. Bibcode:1995PhRvL..75.2787J. doi:10.1103/physrevlett.75.2787. PMID 10059405.
- Kleinert, H., "Critical exponents from seven-loop strong-coupling φ4 theory in three dimensions". Physical Review D 60, 085001 (1999)