Physics:Resummation
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Short description: Technique to acquire finite results from divergent series
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] Feynman and Kleinert's technique has been extended to arbitrary order in quantum mechanics[2] and quantum field theory.[3]
See also
References
- ↑ Feynman R.P., Kleinert H. (1986). "Effective classical partition functions". Physical Review A 34 (6): 5080–5084. doi:10.1103/PhysRevA.34.5080. PMID 9897894. Bibcode: 1986PhRvA..34.5080F. http://www.physik.fu-berlin.de/~kleinert/159/159.pdf.
- ↑ Janke W., Kleinert H. (1995). "Convergent Strong-Coupling Expansions from Divergent Weak-Coupling Perturbation Theory". Physical Review Letters 75 (6): 2787–2791. doi:10.1103/physrevlett.75.2787. PMID 10059405. Bibcode: 1995PhRvL..75.2787J. http://www.physik.fu-berlin.de/~kleinert/228/228.pdf.
- ↑ Kleinert, H., "Critical exponents from seven-loop strong-coupling φ4 theory in three dimensions". 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.
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