1 Classical mechanics 1 --
1.1 Action principle 1 --
1.2 Green functions and the response method 6 --
1.3 Relativistic particle 9 --
2 Quantum mechanics 15 --
2.1 Reminder of the operator approach 15 --
2.2 Path integrals in quantum mechanics 19 --
2.3 Generating functional for Green functions 23 --
2.4 Oscillator as a one-dimensional field theory 26 --
2.5 Need for quantum fields 30 --
3 Free scalar field 33 --
3.1 Lagrange formalism and path integrals for fields 33 --
3.2 Generating functional for a scalar field 34 --
3.3 Green functions for a free scalar field 42 --
3.4 Vacuum energy and the Casimir effect 46 --
4 Scalar field with (Snz(B 4 interaction 51 --
4.1 Perturbation theory for interacting fields 51 --
4.2 Green functions for the (Snz(B 4 theory 53 --
4.A Appendix: Evaluation of Feynman integrals 71 --
5 Global symmetries and Noether's theorem 74 --
5.1 Internal symmetries 74 --
5.2 Noether's theorem 75 --
5.3 Quantum symmetries 79 --
6 Spacetime symmetries 83 --
6.1 Manifolds and tensor fields 84 --
6.2 Covariant derivative and the geodesic equation 87 --
6.3 Integration and Gauss' theorem 92 --
6.4 Symmetries of a general spacetime 94 --
7 Spin-1 and spin-2 fields 98 --
7.4 Source of gravity 109 --
7.A Appendix: Large extra dimensions and massive gravity 110 --
8 Fermions and the Dirac equation 114 --
8.1 Spinor representation of the Lorentz group 114 --
8.2 Dirac equation 117 --
8.3 Quantising Dirac fermions 129 --
8.4 Weyl and Majorana fermions 135 --
9 Scattering processes 140 --
9.1 Unitarity of the S-matrix and its consequences 140 --
9.2 LSZ reduction formula 143 --
9.3 Specific processes 147 --
9.4 Soft photons and gravitons 157 --
9.A Appendix: Decay rates and cross-sections 160 --
10.1 Electrodynamics as abelian gauge theory 168 --
10.2 Non-abelian gauge theories 169 --
10.3 Quantisation of gauge theories 176 --
10.A Appendix: Feynman rules for an unbroken gauge theory 181 --
11 Renormalisation I: Perturbation theory 184 --
11.2 Anomalous magnetic moment of the electron 189 --
11.3 Power counting and renormalisability 196 --
11.4 Renormalisation of the (Snz(B 4 theory 198 --
12 Renormalisation II: Improving perturbation theory 207 --
12.1 Quantum action 207 --
12.2 Ward-Takahashi identities 210 --
12.3 Vacuum polarisation 213 --
12.4 Renormalisation group 219 --
12.5 Renormalisation, critical phenomena and effective theories 225 --
13 Symmetries and symmetry breaking 235 --
13.1 Symmetry breaking and Goldstone's theorem 235 --
13.2 Renormalisation of theories with SSB 241 --
13.3 Abelian Higgs model 246 --
14 GSW model of electroweak interactions 252 --
14.1 Higgs effect and the gauge sector 253 --
14.3 Properties of the Higgs sector 258 --
14.4 Decoupling and the hierarchy problem 262 --
15 Thermal field theory 268 --
15.A Appendix: Equilibrium statistical physics in a nut-shell 278 --
16 Phase transitions and topological defects 281 --
16.1 Phase transitions 281 --
16.2 Decay of the false vacuum 283 --
16.3 Topological defects 288 --
17 Anomalies, instantons and axions 301 --
17.1 Axial anomalies 301 --
17.2 Instantons and the strong CP problem 309 --
18 Hadrons, partons and QCD 319 --
18.1 Trace anomaly and hadron masses 319 --
18.2 DGLAP equations 323 --
18.3 Corrections to e +e - annihilation 331 --
18.A Appendix: Phase-space integrals in DR 337 --
19 Gravity as a gauge theory 340 --
19.1 Vielbein formalism and the spin connection 340 --
19.2 Action of gravity 344 --
19.3 Linearised gravity 348 --
20 Cosmological models for an homogeneous, isotropic universe 355 --
20.2 Friedmann equations 362 --
20.3 Evolution of simple cosmological models 366 --
21.1 Boltzmann equation 373 --
21.2 Thermal relics as dark matter 378 --
21.3 Big bang nucleosynthesis 386 --
22.1 Sakharov conditions and the SM 391 --
22.2 Baryogenesis in out-of-equilibrium decays 396 --
22.3 Baryogenesis in phase transitions 399 --
23 Quantum fields in curved spacetime 403 --
23.1 Conformal invariance and scalar fields 403 --
23.2 Quantisation in curved spacetimes 408 --
23.3 Accelerated observers and the Unruh effect 415 --
24.1 Motivation for inflation 423 --
24.2 Inflation in the homogeneous limit 426 --
24.3 Reheating and preheating 432 --
24.4 Generation of perturbations 436 --
24.5 Outlook: Further evolution of fluctuations 448 --
24.A Appendix: Perturbed Einstein equations 459 --
25.1 Schwarzschild black holes 462 --
25.2 Kerr black holes 471 --
25.3 Black hole thermodynamics and Hawking radiation 475 --
26 Cosmological constant 482 --
26.1 Vacuum energy density 482 --
26.3 Modified gravity 488 --
26.4 Comments on quantising gravity 490.