Non-perturbative Effective Interactions in the Standard Model (eBook)

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Boris A. Arbuzov, Skobeltsyn Institute of Nuclear Physics of Lomonosov Moscow State University,Moscow, Russia.

Preface 5
1 Elementary particles and fields 11
1.1 Conventions and notations 11
1.2 Particles and interactions 12
1.3 Quantum electrodynamics 19
1.4 Quantum chromodynamics 23
1.5 Bethe–Salpeter equation 26
1.6 Effective interactions 28
1.6.1 Preliminaries 28
1.6.2 The model NJL 30
2 The standard model 37
2.1 The electro-weak theory 37
2.1.1 Feynman rules for the electro-weak interaction 50
2.1.2 Higgs scalar search 53
2.2 Status of the standard model 54
2.3 Properties of nonrenormalizable equations, instructive example 59
3 Bogoliubov compensation 67
3.1 Origin of the approach 67
3.2 Application to QFT 68
3.3 A spontaneous generation of the Nambu–Jona-Lasinio interaction 70
3.4 Justification of the model choice 76
3.5 Compensation equation in a six-dimensional scalar model 77
3.6 Bethe–Salpeter equation and zero excitation 86
3.7 Compensation equation for scalar field mass 87
3.8 Estimate of nonlinearity influence 89
3.9 Conclusions of simple scalar model 91
3.10 Appendix 93
4 Three-gluon effective interaction 96
4.1 Compensation equation 96
4.2 Running coupling 103
4.3 The gluon condensate 107
4.4 The glueball 109
4.5 Conclusion 111
5 Nambu–Jona-Lasinio effective interaction 112
5.1 Introduction 112
5.2 Effective NJL interaction 112
5.3 Scalar and pseudo-scalar states 119
5.4 Spontaneous breaking of the chiral symmetry 124
5.5 Pion mass and the quark condensate 126
5.6 Numerical results and discussion 129
5.7 Vector mesons 135
5.7.1 Compensation equations for effective form-factors 136
5.7.2 Wave functions of vector states 142
5.7.3 Results and discussion 148
5.8 Necessary formulae 149
6 Three-boson interaction 151
6.1 Compensation equation for anomalousthree-boson interaction 152
6.2 Effective strong interaction in the weak gauge sector 161
6.3 Scalar bound state of two W-s 163
6.4 Muon g-2 171
7 Possible four-fermion interaction of heavy quarks 177
7.1 Four-fermion interaction of heavy quarks 177
7.2 Doublet bound state .L TR 180
7.3 Stability problem 184
7.4 Possible effects of the heavy quarks interaction 186
8 Overall conclusion 189
8.1 Short review of achievements of the compensation approach 189
8.2 Examples of additional relations in the compensation approach 196
8.3 Weinberg mixing angle and the fine structure constant 206
8.4 Expectations 211
8.5 A possible effective interaction in the general relativity 214
8.6 Appendix 219
Bibliography 229
Index 234

lt;P>"The text provides important background for students and researchers alike, since it gives a useful selection of current research topics in the field of quantum field theory." Zentralblatt für Mathematik