| 1. Lagrangian of the Standard Model | | | |
| 1.1 Gauge theories | | | |
| 1.1.1 Group | | | |
| (1) | | Structure constants |
| (2) | | Anti-symmetric |
| (3) | | Jacoby identity |
| (4) | | Group generators |
| (5) | | Commutation relations |
| (6) | | In the adjoint representation |
| (7) | | Representation of the Group transformation |
| (8) | | Orthonormal condition |
| 1.1.2 Local gauge invariance | | | |
| (1) | | Point in the space-time manifold |
| (2) | | Gauge fields |
| (3) | | Matter fields |
| (4) | | Operator performing an infenitesimal transformation of fields under the local gauge transformation |
| (5) | | Transformation of matter fields |
| (6) | | Local gauge transformation for gauge fields |
| (7) | | Covariant derivative |
| (8) | | Gauge field tensor |
| (9) | | |
| (10) | | |
| (11) | | Coupling constant |
| (12) | | Lagrangian of the matter field which is invariant under the global gauge transformation |
| (13) | | General Lagrangian of a gauge theory |
| 1.1.3 Gauge fixing terms | | | |
| (1) | | General form of the gauge fixing term |
| (2) | | Faddeev-Popov ghosts |
| (3) | | Faddeev-Popov Lagrangian term |
| (4) | | Feynman-like gauge Lagrangian term |
| (5) | | quadratic part of the gauge field Lagrangian |
| (6) | | Faddeev-Popov Lagrangian term |
| (7) | | Normalization of LFP |
| 1.1.4 Normalization | | | |
| (1) | | Rescaling for applying perturbation theory |
| 1.2 QCD Lagrangian; gauge theory based on the SU(3) group | | | |
| (1) | | Gluon gauge field |
| (2) | | Quark matter field (k=1,2,3) |
| (3) | | Faddeev-Popov ghosts |
| (4) | | Coupling constant |
| (5) | | SU(3) Structure constants |
| (6) | | Gell-Mann matrices |
| (6a) | | |
| (6b) | | |
| (6c) | | |
| (6d) | | |
| (6e) | | |
| (6f) | | |
| (6g) | | |
| (6h) | | |
| (7) | | Generators in the fundamental representation |
| (8) | | QCD Lagrangian in the Feynnmann gauge |
| (9) | | Covariant derivative |
| (10) | | Gauge field tensor |
| (11) | | Feynman-like gauge Lagrangian term |
| (12) | | Faddeev-Popov Lagrangian term |
| 1.3 Lagrangian of electroweak interactions; gauge theory based on the SU(2)xU(1) group | | | |
| 1.3.1 Vector bosons | | | |
| (1) | | Triplet of SU(2) vector field |
| (2) | | Sigle of U(1) vector field |
| (3) | | SU(2) structure constante antisimetric tensor (Levi-Civita tensor) |
| (4) | | Coupling constant for the SU(2) gauge interaction |
| (5) | | Gauge field |
| (6) | | Gauge field |
| (7) | | Lagrangian of the gauge fields |
| (8) | | Infinitesimal local gauge transformations |
| (9) | | Infinitesimal local gauge transformations |
| (10) | | Infinitesimal local gauge transformations |
| (11) | | Infinitesimal local gauge transformations |
| (12) | | Lagrangian of self-interaction for the SU(2) gauge fields in terms of W's |
| (13) | | Pauli Matrices |
| (13a) | | |
| (13a) | | |
| (13a) | | |
| (14) | | Generators for the doublets |
| (15) | | Coupling constant for the U(1) gauge interaction |
| (16) | | Hypercharge |
| (17) | | Infinitesimal local gauge transformations for doublets |
| (18) | | Y=1 vacuum state Higgs doublet |
| (19) | | Real constant |
| (20) | | Photon field |
| (21) | | Mixing Angle |
| (22) | | Z field |
| 1.3.2 Lagrangian of Higgs field | | | |
| 1.3.3 Gauge fixing and ghost terms for the t'Hooft-Feynman gauge | | | |
| 1.3.4 Unitary gauge | | | |
| 1.3.5 Summary of vertices for the boson sector | | | |
| 1.3.6 Interaction of vector bosons with fermions | | | |
| 1.3.7 Interaction of the Higgs doublet with fermions and generation of fermion masses | | | |
| 1.3.8 Quarks and leptons | | | |
| 2 Ghost fields | | | |
| 3 QED processes | | | |
Elementary Particles
