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.[1] In quantum mechanics it was extended to any order here,[2] and in quantum field theory here.[3] See also Chapters 16–20 in the textbook cited below.
References
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)
Books
Hagen Kleinert, Critical Properties of φ4-Theories, World Scientific (Singapore, 2001); Paperback ISBN 981-02-4658-7 (also available online) (together with V. Schulte-Frohlinde).
Hellenica World - Scientific Library
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