Large-Order Behaviour of Perturbation Theory - 1st Edition - ISBN: 9780444885975, 9780444596208

Large-Order Behaviour of Perturbation Theory, Volume 7

1st Edition

eBook ISBN: 9780444596208
Imprint: North Holland
Published Date: 30th April 2013
Sales tax will be calculated at check-out Price includes VAT/GST
Price includes VAT/GST
× DRM-Free

Easy - Download and start reading immediately. There’s no activation process to access eBooks; all eBooks are fully searchable, and enabled for copying, pasting, and printing.

Flexible - Read on multiple operating systems and devices. Easily read eBooks on smart phones, computers, or any eBook readers, including Kindle.

Open - Buy once, receive and download all available eBook formats, including PDF, EPUB, and Mobi (for Kindle).

Institutional Access

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.

Table of Contents

Introduction. References. Papers: 1. Methods and Simple Examples. 2. More Complex Systems. 3. Field Theories with Fermions. 4. Large-Order Behaviour: Difficulties, Applications. 5. Additional References. 6. General Articles: Aims and Methods in the Simplest Cases. Contributors: G. Auberson, C.M. Bender, E.B. Bogomolny, E. Brézin, J.C. Collins, F.J. Dyson, C.S. Lam, J.S. Langer, J.C. Le Guillou, L.N. Lipatov, G. Mahoux, G. Mennessier, G. Parisi, P.E. Soper, T.T. Wu, J. Zinn-Justin, J. Zittartz. 7. Determinations of the Large Order Behaviour in more Complex Situations: Quantum Mechanics. Contributors: B.G. Adams, J.E. Avron, L. Benassi, E.B. Bogomolny, E. Brézin, J. Cizek, M. Clay, R.J. Damburg, M.L. Glasser, S. Graffi, V. Grecchi, E. Harrell, I.W. Herbst, S.C. Kanavi, J.C. Le Guillou, V. Martyshchenko, R.K. Moats, P. Otto, J. Paldus, G. Parisi, S.H. Patil, R.Kh. Propin, H.J. Silverstone, B. Simon, E. Vrscay, J. Zinn-Justin. Field Theory without Fermions. Contributors: J. Avan, E.B. Bogomolny, E. Brézin, A.P. Buchvostov, V.A. Fateyev, S. Hikami, A. Houghton, C. Itzykson, L.N. Lipatov, E.I. Malkov, G. Parisi, J.S. Reeve, H.J. de Vega, D.J. Wallace, J.B. Zuber. Field Theory with Fermions. Contributors: R. Balian, E.B. Bogomolny, V.A. Fateyev, M.P. Fry, C. Itzykson, T. Kinoshita, Yu.A. Kubyshin, W.B. Lindquist, G. Parisi, J.B. Zuber. 8. The Renormalons. Contributors: M.C. Bergère, S. Chadha, F. David, B. Lautrup, P. Olesen, G. Parisi. 9. Physical Applications of the Large-Order Behaviour to the Summation of Divergent Series. Contributors: G.A. Baker, A. Berkovich, M.S. Green, J.C. Le Guillou, J.J. Loeffel, J.H. Lowenstein, D.I. Meiron, B.G. Nickel, J. Zinn-Justin.


This volume is concerned with the determination of the behaviour of perturbation theory at large orders in quantum mechanics and quantum field theory, and its application to the problem of summation of perturbation series.

Perturbation series in quantum field theory and in many quantum mechanics models are only asymptotic and thus diverge for all values of the expansion parameter. Their behaviour at large orders provides information about whether they define the theory uniquely (the problem of Borel summability). It suggests methods to extract numerical information from the series when the expansion parameter is not small.

The articles reprinted here deal with the explicit evaluation of large-order behaviour in many quantum mechanics and field theory models. The large-order behaviour is related to barrier penetration effects for unphysical values of the expansion parameter, which can be calculated by WKB or instanton methods. The calculation of critical exponents of &fgr;4 field theory is presented as a practical application.


© North Holland 1990
North Holland
eBook ISBN:

Ratings and Reviews