Large-Order Behaviour of Perturbation Theory
- 1st Edition, Volume 7 - June 20, 1990
- Imprint: North Holland
- Editors: J.C. Le Guillou, J. Zinn-Justin
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 4 - 8 8 5 9 7 - 5
- Hardback ISBN:9 7 8 - 0 - 4 4 4 - 8 8 5 9 4 - 4
- eBook ISBN:9 7 8 - 0 - 4 4 4 - 5 9 6 2 0 - 8
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… Read more
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Request a sales quoteThis 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.
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.
- Edition: 1
- Volume: 7
- Published: June 20, 1990
- Imprint: North Holland
- Language: English
- Paperback ISBN: 9780444885975
- Hardback ISBN: 9780444885944
- eBook ISBN: 9780444596208
JZ
J. Zinn-Justin
Affiliations and expertise
CEN Saclay, Gif-sur-Yvette, FranceRead Large-Order Behaviour of Perturbation Theory on ScienceDirect