Large-Order Behaviour of Perturbation Theory, Volume 7

1st Edition

Editors: J.C. Le Guillou J. Zinn-Justin
Paperback ISBN: 9780444885975
eBook ISBN: 9780444596208
Imprint: North Holland
Published Date: 30th April 2013
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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.

Description

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.


Details

Language:
English
Copyright:
© North Holland 1990
Published:
Imprint:
North Holland
eBook ISBN:
9780444596208
Hardcover ISBN:
9780444885944
Paperback ISBN:
9780444885975

About the Editors

J.C. Le Guillou Editor

J. Zinn-Justin Editor

Affiliations and Expertise

CEN Saclay, Gif-sur-Yvette, France