| Preface |
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vii | |
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1 The Principles of Quantum Physics |
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1 | (8) |
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1.1 Principles shared by QM and QFT |
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1 | (2) |
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1.2 Principles of NRQM not shared by QFT |
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3 | (6) |
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2 Lorentz Group and Hilbert Space |
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9 | (18) |
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2.1 Defining properties of Lorentz transformations |
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9 | (3) |
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2.2 Classification of Lorentz transformations |
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12 | (2) |
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2.3 Lie algebra of the Lorentz group |
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14 | (3) |
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2.4 Finite irreducible representation of L |
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17 | (3) |
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2.5 Transformation properties of massive 1-particle states |
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20 | (3) |
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2.6 Transformation properties of zero-mass 1-particle states |
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23 | (4) |
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3 Search for a Relativistic Wave Equation |
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27 | (9) |
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3.1 A relativistic Schrodinger equation |
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27 | (2) |
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3.2 Difficulties with the wave equation |
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29 | (3) |
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3.3 The Klein--Gordon equation |
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32 | (1) |
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3.4 KG equation in the presence of an electromagnetic field |
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33 | (3) |
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36 | (18) |
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4.1 Dirac spinors in the Dirac and Weyl representations |
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36 | (8) |
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4.2 Properties of the Dirac spinors |
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44 | (1) |
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4.3 Properties of the γ-matrices |
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45 | (2) |
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4.4 Zero-mass, spin = 1/2 fields |
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47 | (4) |
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51 | (3) |
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54 | (4) |
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5.1 The radiation field in the Lorentz gauge |
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54 | (2) |
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5.2 The radiation field in the Coulomb gauge |
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56 | (2) |
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6 Quantum Mechanics of Dirac Particles |
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58 | (16) |
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6.1 Probability interpretation |
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58 | (3) |
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6.2 Non-relativistic limit |
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61 | (1) |
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6.3 Negative-energy solutions and localization |
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62 | (2) |
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64 | (3) |
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6.5 Foldy--Wouthuysen Transformation |
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67 | (7) |
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74 | (16) |
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7.1 Fock-space representation of fields |
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74 | (8) |
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7.2 Commutation relations |
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82 | (3) |
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7.3 P, C, T from equations of motion |
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85 | (3) |
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7.4 P, C, T in second quantization |
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88 | (2) |
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90 | (17) |
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8.1 Lagrangian formulation and Euler-Lagrange equations |
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90 | (5) |
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8.2 Canonical quantization: unconstrained systems |
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95 | (3) |
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8.3 Canonical quantization: constrained systems |
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98 | (3) |
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8.4 QED as a constrained system |
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101 | (6) |
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9 Global Symmetries and Conservation Laws |
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107 | (10) |
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107 | (3) |
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110 | (2) |
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9.3 Translational invariance |
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112 | (2) |
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9.4 Lorentz transformations |
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114 | (3) |
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117 | (17) |
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10.1 The S-matrix and T-matrix |
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118 | (4) |
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10.2 Differential cross-section |
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122 | (5) |
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10.3 LSZ reduction formula |
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127 | (7) |
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134 | (32) |
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11.1 Interaction picture and U-matrix |
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134 | (2) |
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11.2 Interaction picture representation of Green functions |
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136 | (3) |
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139 | (3) |
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142 | (6) |
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11.5 Feynman Diagrams for QED |
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148 | (5) |
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153 | (1) |
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11.7 Going over to momentum space |
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154 | (2) |
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11.8 Momentum space Feynman rules for QED |
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156 | (1) |
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157 | (3) |
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11.10 The Moeller differential cross-section |
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160 | (3) |
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163 | (3) |
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12 Parametric Representation of a General Diagram |
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166 | (13) |
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12.1 Cutting rules for a general diagram |
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166 | (6) |
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12.2 An alternative approach to cutting rules |
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172 | (3) |
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12.3 4-point function in the ladder approximation |
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175 | (4) |
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179 | (34) |
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13.1 The Generating Functional |
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180 | (1) |
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13.2 Schwinger's Construction of Z[ j] |
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180 | (4) |
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13.3 Feynman Path-Integral |
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184 | (5) |
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13.4 Path-integral representation of correlators in QM |
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189 | (5) |
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13.5 Feynman path-integral representation in QFT |
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194 | (4) |
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13.6 Path-Integral for Grassman-valued fields |
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198 | (6) |
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13.7 Extension to Field Theory |
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204 | (2) |
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13.8 Mathews--Salam representation of QED generating functional |
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206 | (3) |
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13.9 Faddeev--Popov quantization and α-gauges |
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209 | (4) |
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14 Dyson--Schwinger Equation |
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213 | (7) |
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14.1 Classification of Feynman Diagrams |
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213 | (2) |
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14.2 Basic building blocks of QED |
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215 | (3) |
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14.3 Dyson--Schwinger Equations |
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218 | (2) |
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15 Regularization of Feynman Diagrams |
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220 | (16) |
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15.1 Pauli--Villars and dimensional regularization |
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220 | (16) |
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15.1.1 Electron self-energy |
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222 | (4) |
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15.1.2 Photon vacuum polarization |
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226 | (5) |
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15.1.3 The vertex function |
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231 | (5) |
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236 | (37) |
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16.1 The principles of renormalization |
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237 | (3) |
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16.2 Renormalizability of QED |
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240 | (6) |
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16.2.1 Fermion 2-point function |
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242 | (2) |
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16.2.2 Photon 2-point function |
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244 | (1) |
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245 | (1) |
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16.3 Ward--Takahashi Identity and overlapping divergences |
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246 | (5) |
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16.4 1-loop renormalization in QED |
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251 | (4) |
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16.5 Composite operators and Wilson expansion |
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255 | (1) |
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16.6 Criteria for renormalizability |
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256 | (4) |
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260 | (3) |
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16.8 Bogoliubov's recursion formula |
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263 | (1) |
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16.9 Overlapping divergences |
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264 | (3) |
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16.10 Dispersion relations: a brief view |
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267 | (6) |
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17 Broken Scale Invariance and Callan--Symanzik Equation |
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273 | (30) |
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17.1 Scale transformations |
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274 | (3) |
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17.2 Unrenormalized Ward identities of broken scale invariance |
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277 | (3) |
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17.3 Broken scale invariance and renormalized Ward identities |
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280 | (3) |
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283 | (3) |
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17.5 Solution of CS equation in the deep euclidean region |
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286 | (4) |
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17.6 Asymptotic behaviour of T and zeros of the β-function |
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290 | (3) |
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17.7 Perturbative calculation of β(g) and 7(3) in φ4 theory |
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293 | (5) |
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17.8 QED β-function and anomalous dimension |
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298 | (1) |
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17.9 QED β-function and leading log summation |
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299 | (2) |
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17.10 Infrared fix point of QED and screening of charge |
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301 | (2) |
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303 | (8) |
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18.1 The Renormalization Group equation |
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303 | (6) |
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18.2 Asymptotic solution of RG equation |
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309 | (2) |
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19 Spontaneous Symmetry Breaking |
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311 | (10) |
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311 | (2) |
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19.2 More about spontaneous symmetry breaking |
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313 | (3) |
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19.3 The Goldstone Theorem |
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316 | (2) |
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19.4 Realization of Goldstone Theorem in QFT |
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318 | (3) |
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321 | (14) |
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20.1 Generating functional of proper functions |
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321 | (3) |
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20.2 The effective potential |
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324 | (1) |
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20.3 The 1-loop effective potential of φ4-theory |
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325 | (2) |
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20.4 WKB approach to the effective potential |
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327 | (2) |
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20.5 The effective potential and SSB |
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329 | (6) |
| Index |
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335 | |
Lisainfo e-raamatute kohta