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SIGMA 5 (2009), 005, 10 pages arXiv:0901.1858
https://doi.org/10.3842/SIGMA.2009.005
Contribution to the Proceedings of the VIIth Workshop ''Quantum Physics with Non-Hermitian Operators''
Generalized Nonanalytic Expansions, PT-Symmetry and Large-Order Formulas for Odd Anharmonic Oscillators
Ulrich D. Jentschura a, Andrey Surzhykov b and Jean Zinn-Justin c
a) Department of Physics, Missouri University of Science
and Technology, Rolla MO65409-0640, USA
b) Physikalisches Institut der Universität, Philosophenweg 12, 69120 Heidelberg, Germany
c) CEA, IRFU and Institut de Physique Théorique, Centre de Saclay, F-91191 Gif-Sur-Yvette, France
Received October 30, 2008, in final form January 07, 2009; Published online January 13, 2009
Abstract
The concept of a generalized nonanalytic expansion
which involves nonanalytic combinations of exponentials,
logarithms and powers of a coupling is introduced and its use
illustrated in various areas of physics.
Dispersion relations for the resonance energies of odd anharmonic
oscillators are discussed, and higher-order formulas are presented
for cubic and quartic potentials.
Key words:
PT-symmetry; asymptotics; higher-order corrections; instantons.
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