|
Teoreticheskaya i Matematicheskaya Fizika, 1988, Volume 75, Number 2, Pages 234–244
(Mi tmf4777)
|
|
|
|
Borel summation of divergent series in field theory and Wynn's $\varepsilon$ algorithm
I. O. Maier
Abstract:
The first confluent form of Wynn's $\varepsilon$ algorithm is used in the Borel
summation of some divergent perturbation-theory series that satisfy
a strong asymptotic condition. The summation procedure reduces to the
calculation of a sequence of ratios of Hankel functional determinants
composed of a Borel integral and its derivatives and can be regarded
as an alternative to the Padé and Padé–Borel methods. It admits a simple generalization to the summation of multiple series. The perturbation series for the ground-state energy of the anharmonic oscillator, Yukawa potential, and charmonium potential are analyzed; the critical
exponents of the $O(n)$-symmetric $\varphi^4$ theories (models of phase transitions)
for $n=0,1,2,3$ and the dilute Ising model are determined.
Received: 01.10.1986
Citation:
I. O. Maier, “Borel summation of divergent series in field theory and Wynn's $\varepsilon$ algorithm”, TMF, 75:2 (1988), 234–244; Theoret. and Math. Phys., 75:2 (1988), 493–501
Linking options:
https://www.mathnet.ru/eng/tmf4777 https://www.mathnet.ru/eng/tmf/v75/i2/p234
|
Statistics & downloads: |
Abstract page: | 375 | Full-text PDF : | 183 | References: | 40 | First page: | 1 |
|