Quantum electrodynamic bound state calculations and large order perturbation theory

I Quantum Electrodynamic Bound--State Calculations......Page 7
1.2 Introduction to the Numerical Calculation of Radiative Corrections......Page 8
1.3.1 Status of Analytic Calculations......Page 9
1.3.2 Formulation of the Numerical Problem......Page 12
1.3.3 Treatment of the divergent terms......Page 15
1.4.1 The Infrared Part......Page 17
1.4.2 The Middle-Energy Subtraction Term......Page 21
1.4.3 The Middle-Energy Remainder......Page 22
1.5.1 The High-Energy Subtraction Term......Page 25
1.5.2 The High-Energy Remainder......Page 27
1.6 Comparison to Analytic Calculations......Page 29
2.1 Orientation......Page 34
2.2 The epsilon-Method......Page 35
2.3.1 P_1/2 states (kappa = 1)......Page 37
2.3.2 P_3/2 states (kappa = -2)......Page 38
2.3.4 D_5/2 states (kappa = -3)......Page 39
2.3.6 F_7/2 states (kappa = -4)......Page 40
2.5 Typical Cancellations......Page 41
2.6 Observations......Page 42
3.2 Introduction to the Two--Loop Self--Energy......Page 45
3.3 Two-loop Form Factors......Page 47
3.4 High--Energy Part......Page 50
3.5 Low--Energy Part......Page 52
3.6 Results for the Two--Loop Corrections......Page 55
4.3 Breit hamiltonian for Spinless Particles......Page 56
4.5 Effects due to Scalar QED......Page 60
5 QED Calculations: A Summary......Page 63
II Convergence Acceleration and Divergent Series......Page 67
6 Introduction to Convergence Acceleration and Divergent Series in Physics......Page 68
7.1.1 A Brief Survey......Page 71
7.1.3 Linear and Logarithmic Convergence......Page 72
7.1.4 The Standard Tool: Padé Approximants......Page 73
7.1.5 Nonlinear Sequence Transformations......Page 74
7.1.6 The Combined Nonlinear--Condensation Transformation (CNCT)......Page 77
7.2.1 Applications in Statistics and Applied Biophysics......Page 79
7.2.2 An Application in Experimental Mathematics......Page 80
7.3 Conclusions and Outlook for Convergence Acceleration......Page 84
8.1 Introduction to Divergent Series in Physics......Page 86
8.2.1 Perturbation Series for the Stark Effect......Page 87
8.2.2 Borel--Padé Resummation......Page 88
8.2.3 Doubly--Cut Borel Plane......Page 90
8.2.4 Numerical Calculations for the Stark Effect......Page 92
8.3.1 Zero--Dimensional Theories with Degenerate Minima......Page 95
8.3.2 The Effective Action as a Divergent Series......Page 98
8.3.3 The Double--Well Problem......Page 103
8.4 Divergent Series: Some Conclusions......Page 108
9 Conclusions......Page 111