Table of Contents
Preface v
1 Elementary particles and fields 1
1.1 Conventions and notations 1
1.2 Particlesand interactions 2
1.3 Quantum electrodynamics 9
1.4 Quantum chromodynamics 13
1.5 Bethe-Salpeter equation 16
1.6 Effective interactions 18
1.6.1 Preliminaries 18
1.6.2 The model NJL 20
2 The standard model 27
2.1 The electro-weak theory 27
2.1.1 Feynman rules for the electro-weak interaction 40
2.1.2 Higgs scalar search 43
2.2 Status of the standard model 44
2.3 Properties of nonrenormalizable equations, instructive example 49
3 Bogoliubov compensation 57
3.1 Origin of the approach 57
3.2 Application to QFT 58
3.3 A spontaneous generation of the Nambu-jona-Lasinio interaction 60
3.4 Justification of the model choice 66
3.5 Compensation equation in a six-dimensional scalar model 67
3.6 Bethe-Salpeter equation and zero excitation 76
3.7 Compensation equation for scalar field mass 77
3.8 Estimate of nonlinearity influence 79
3.9 Conclusions of simple scalar model 81
3.10 Appendix 83
4 Three-gluon effective interaction 86
4.1 Compensation equation 86
4.2 Running coupling 93
4.3 The gluon condensate 97
4.4 The glueball 99
4.5 Conclusion 101
5 Nambu-Jona-Lasinio effective interaction 102
5.1 Introduction 102
5.2 Effective NJL interaction 102
5.3 Scalar and pseudo-scalar states 109
5.4 Spontaneous breaking of the chiral symmetry 114
5.5 Pion mass and the quark condensate 116
5.6 Numerical results and discussion 119
5.7 Vector mesons 125
5.7.1 Compensation equations for effective form-factors 126
5.7.2 Wave functions of vector states 132
5.7.3 Results and discussion 138
5.8 Necessary formulae 139
6 Three-boson interaction 141
6.1 Compensation equation for anomalous three-boson interaction 142
6.2 Effective strong interaction in the weak gauge sector 151
6.3 Scalar bound state of two W-s 153
6.4 Muon g-2 161
7 Possible four-fermion interaction of heavy quarks 167
7.1 Four-fermion interaction of heavy quarks 167
7.2 Doublet bound state ΨL TR 170
7.3 Stability problem 174
7.4 Possible effects of the heavy quarks interaction 176
8 Overall conclusion 179
8.1 Short review of achievements of the compensation approach 179
8.2 Examples of additional relations in the compensation approach 186
8.3 Weinberg mixing angle and the fine structure constant 196
8.4 Expectations 201
8.5 A possible effective interaction in the general relativity 204
8.6 Appendix 209
Bibliography 219
Index 224
