Large-Order Behaviour of Perturbation Theory

Content: 
Current Physics — Sources and Comments
Page ii

Front Matter
Page iii

Copyright page
Page iv

Preface
Pages v-vi
J.-C. Le Guillou, J. Zinn-Justin

Acknowledgements
Pages vii-ix

1 - Methods and Simple Examples
Pages 1-12

2 - More Complex Systems
Pages 13-18

3 - Field Theories with Fermions
Pages 19-21

4 - Large-Order Behaviour: Difficulties, Applications
Pages 23-25

5 - Additional references
Page 27

6 - General articles
Pages 29-31

Divergence of Perturbation Theory in Quantum Electrodynamics
Pages 32-33
F.J. DYSON

Theory of Bound States in a Random Potential
Pages 34-40
J. ZITTARTZ, J.S. LANGER

Anharmonic Oscillator. II. A Study of Perturbation Theory in Large Order
Pages 41-57
Carl M. Bender, Tai Tsun Wu

Physical Review Letters: Statistical Analysis of Feynman Diagrams
Pages 58-61
Carl M. Bender, Tai Tsun Wu

Behavior of Very-High-Order Perturbation Diagrams
Pages 62-78
C.S. LAM

Divergence of the perturbation-theory series and pseudoparticles
Pages 79-82
L.N. Lipatov

Divergence of the perturbation-theory series and the quasi-classical theory
Pages 83-90
L.N. Lipatov

Perturbation theory at large order. I. The Φ2N interaction
Pages 91-104
E. Brézin, J.C. Le Guillou, J. Zinn-Justin

Perturbation theory at large order. II. Role of the vacuum instability
Pages 105-111
E. Brézin, J.-C. Le Guillou, J. Zinn-Justin

Asymptotic Estimates in Perturbation Theory
Pages 112-114
G. PARISI

Calculation of the Green Functions by the Coupling Constant Dispersion Relations
Pages 115-116
E.B. BOGOMOLNY

Asymptotic Estimates of Feynman Diagrams
Pages 117-120
G. PARISI

Large Order Expansion in Perturbation Theory
Pages 121-146
JOHN C. COLLINS, DAVISON E. SOPER

On the Perturbation Theory of the Anharmonic Oscillator at Large Orders
Pages 147-169
G. AUBERSON, G. MENNESSIER, G. MAHOUX

Perturbation theory at large orders for a potential with degenerate minima
Pages 170-174
E. Brézin, G. Parisi, J. Zinn-Justin

Calculation of Instanton–Anti-Instanton Contributions in Quantum Mechanics
Pages 175-179
E.B. BOGOMOLNY

Expansion around instantons in quantum mechanics
Pages 180-189
J. Zinn-Justin

Multi-Instanton Contributions in Quantum Mechanics
Pages 190-205
J. ZINN-JUSTIN

Multi-Instanton Contributions in Quantum Mechanics (II)
Pages 206-221
J. ZINN-JUSTIN

Instantons in quantum mechanics: Numerical evidence for a conjecture
Pages 222-228
J. Zinn-Justin

Large-order perturbation theory for the O(2) anharmonic oscillator with negative anharmonicity and for the double-well potential
Pages 229-239
R Damburg, R Propint, V Martyshchenko

Borel Summability: Application to the Anharmonic Oscillator
Pages 240-243
S. GRAFFI, V. GRECCHI, B. SIMON

The Zeeman Effect Revisited
Pages 244-246
J. AVRON, I. HERBST, B. SIMON

Bender-Wu Formula, the SO(4,2) Dynamical Group, and the Zeeman Effect in Hydrogen
Pages 247-249
J.E. Avron, B.G. Adams, J. Čížek, M. Clay, M.L. Glasser, P. Otto, J. Paldus, E. Vrscay

Dispersion Relations for the Zeeman Effect in the Hydrogen Atom
Pages 250-255
S.C. KANAVI, S.H. PATIL

Bender-Wu formulas for degenerate eigenvalues
Pages 256-258
B.G. Adams, J.E. Avron, J. Čížek, P. Otto, J. Paldus, R.K. Moats, H.J. Silverstone

The Hydrogen Atom in Strong Magnetic Fields: Summation of the Weak Field Series Expansion
Pages 259-286
J.C. LE GUILLOU, J. ZINN-JUSTIN

Physical Review Letters: Stark Effect Revisited
Pages 287-289
I.W. Herbst, B. Simon

Bender-Wu Formula and the Stark Effect in Hydrogen
Pages 290-293
L. Benassi, V. Grecchi, E. Harrell, B. Simon

Errata
Page 294

Expansion of the H2+ ground state energy in inverse powers of the distance between the two protons
Pages 295-296
E. Brézin, J. Zinn-Justin

1/R Expansion for H2+: Analyticity, Summability, Asymptotics, and Calculation of Exponentially Small Terms
Pages 297-300
Robert J. Damburg, Rafail Kh. Propin, Sandro Graffi, Vincenzo Grecchi, Evans M. Harrell II, Jiří Čížek, Josef Paldus, Harris J. Silverstone

Asymptotic Estimates in Scalar Electrodynamics
Pages 301-305
C. Itzykson, G. Parisi, J.B. Zuber

High Orders of the Perturbation Theory in Scalar Electrodynamics
Pages 306-308
A.P. BUCHVOSTOV, L.N. LIPATOV

Asymptotic estimates of high order perturbation theory approximations in scalar electrodynamics
Pages 309-317
A.P. Bukhvostov, L.N. Lipatov

Large Order Calculations in Gauge Theories
Pages 318-321
E.B. BOGOMOLNY, V.A. FATEYEV

Large-order estimates for perturbation theory of a Yang-Mills field coupled to a scalar field
Pages 322-331
L.N. Lipatov, A.P. Bukhvostov, E.I. Malkov

High-order behavior in Φ3 field theories and the percolation problem
Pages 332-340
A. Houghton, J.S. Reeve, D.J. Wallace

Large-order behaviour of the 1/N expansion in zero and one dimensions
Pages 341-352
S Hikami, E Brézin

The Non-Linear Sigma Model in the 1/N Expansion and the Inverse Scattering Transformation in the Angular Momentum
Pages 353-357
H.J. de VEGA

Classical solutions by inverse scattering transformation in any number of dimensions. I. The gap equation and the effective action
Pages 358-370
J. Avan, H.J. de Vega

Classical solutions by inverse scattering transformation in any number of dimensions. II. Instantons and large orders of the 1/N series for the  theory in v dimensions (1 ≤ v ≤ 4)
Pages 371-382
J. Avan, H.J. de Vega

Asymptotic Estimates in Perturbation Theory with Fermions
Pages 383-385
G. PARISI

Asymptotic estimates in quantum electrodynamics
Pages 386-403
C. Itzykson, G. Parisi, J-B. Zuber

Asymptotic estimates in quantums electrodynamics. II
Pages 404-415
R. Balian, C. Itzykson, J.B. Zuber, G. Parisi

The Dyson Instability and Asymptotics of the Perturbation Series in QED
Pages 416-418
E.B. BOGOMOLNY, V.A. FATEYEV

Asymptotic estimates for graphs with a fixed number of fermion loops in quantum electrodynamics. The choice of the form of the steepest-descent solutions
Pages 419-424
E.B. Bogomol'ny, Yu.A. Kubyshin

Asymptotic estimates for diagrams with a fixed number of fermion loops in quantum electrodynamics. The extremal configurations with the symmetry group O(2) ⊗ O(3)
Pages 425-430
E.B. Bogomol'nyi, Yu. A. Kubyshin

Eighth-Order Anomalous Magnetic Moment of the Electron
Pages 431-434
T. Kinoshita, W.B. Lindquist

Vacuum Energy Density in Large Orders of Perturbation Theory for the Scalar Yukawa2 Field Theory
Pages 435-437
M.P. FRY

On High Order Estimates in QED
Pages 438-440
B. LAUTRUP

On Borel Singularities in Quantum Field Theory
Pages 441-444
S. CHADHA, P. OLESEN

On Vacuum Instability in Quantum Field Theory
Pages 445-447
P. OLESEN

Singularities of the Borel Transform in Renormalizable Theories
Pages 448-449
G. PARISI

Ambiguities of Renormalized Φ44 Field Theory and the Singularities of its Borel Transform
Pages 450-454
M.C. BERGÈRE, F. DAVID

On Infrared Divergences
Pages 455-464
G. PARISI

Non-Perturbative Effects and Infrared Renormalons within the 1/N Expansion of the O(N) Non-Linear Sigma Model
Pages 465-492
F. DAVID

On the Ambiguity of Composite Operators, ir Renormalons and the Status of the Operator Product Expansion
Pages 493-507
F. DAVID

The Operator Product Expansion and Renormalons: A Comment
Pages 508-519
F. DAVID

Physical Review Letters: Ising-Model Critical Indices in Three Dimensions from the Callan-Symanzik Equation
Pages 520-523
George A. Baker Jr., Bernie G. Nickel, Melville S. Green, Daniel I. Meiron

Workshop on Padé approximants
Page 524

Transformation of an asymptotic series in a convergent one
Pages 525-526
J.J. LOEFFEL

Critical Exponents for the n-Vector Model in Three Dimensions from Field Theory
Pages 527-530
J.C. Le Guillou, J. Zinn-Justin

Critical exponents from field theory
Pages 531-553
J.C. Le Guillou, J. Zinn-Justin

Accurate critical exponents from the ε-expansion
Pages 554-558
J.C. Le Guillou, J. Zinn-Justin

Accurate critical exponents for Ising like systems in non-integer dimensions
Pages 559-564
J.C. Le Guillou, J. Zinn Justin

Le Journal de Physique: Accurate critical exponents from field theory
Pages 565-570
J.C. Le Guillou, J. Zinn-Justin

Essentially perturbative quantities in the Kondo model
Pages 571-580
A. Berkovich, J.H. Lowenstein