Preface |
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vi | |
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1 | (11) |
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One-Dimensional Harmonic Crystal |
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1 | (6) |
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1 | (3) |
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4 | (1) |
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Annihilation and Creation Operators for Normal Modes |
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5 | (2) |
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7 | (5) |
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7 | (1) |
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8 | (4) |
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Relativistic Scalar Fields |
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12 | (13) |
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12 | (1) |
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The Klein-Gordon Equation |
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13 | (5) |
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Relativistic Normalization |
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14 | (2) |
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16 | (1) |
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17 | (1) |
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Symmetries and Noether's Theorem |
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18 | (7) |
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18 | (3) |
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21 | (4) |
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25 | (12) |
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25 | (1) |
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26 | (4) |
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26 | (1) |
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Propagators and Time-Ordered Products |
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27 | (3) |
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30 | (7) |
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30 | (1) |
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30 | (2) |
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32 | (5) |
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37 | (11) |
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37 | (6) |
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37 | (4) |
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Diagrams in Momentum Space |
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41 | (2) |
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43 | (5) |
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44 | (3) |
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Decay of an Unstable Particle |
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47 | (1) |
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Loops, Unitarity, and Analyticity |
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48 | (14) |
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Unitarity of the S Matrix |
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48 | (3) |
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51 | (5) |
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51 | (1) |
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Unitarity and Branch Cuts |
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52 | (2) |
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Resonances, Widths, and Lifetimes |
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54 | (2) |
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56 | (6) |
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56 | (2) |
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58 | (1) |
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Dimensional Regularization |
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59 | (3) |
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62 | (10) |
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62 | (2) |
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Lehmann-Kallen Spectral Representation |
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64 | (3) |
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67 | (5) |
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Amputation of External Legs |
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67 | (1) |
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In and Out States and Fields |
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68 | (3) |
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71 | (1) |
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72 | (11) |
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72 | (2) |
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Spinors, Tensors, and Currents |
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74 | (1) |
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74 | (1) |
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75 | (1) |
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75 | (4) |
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Positive and Negative Energies |
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75 | (3) |
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78 | (1) |
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79 | (4) |
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Normal and Time-Ordered Products |
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81 | (2) |
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83 | (14) |
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Quantizing Maxwell's Equations |
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83 | (5) |
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83 | (1) |
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84 | (1) |
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85 | (3) |
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88 | (4) |
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90 | (2) |
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Ward Identity and Gauge Invariance |
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92 | (5) |
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92 | (1) |
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93 | (4) |
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97 | (20) |
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97 | (3) |
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Fermi Gas and Fermi Liquid |
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100 | (14) |
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One-Particle Density Matrix |
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100 | (3) |
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103 | (1) |
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104 | (2) |
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106 | (8) |
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114 | (3) |
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117 | (19) |
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117 | (1) |
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Spontaneous Symmetry Breaking |
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118 | (4) |
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122 | (9) |
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122 | (3) |
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125 | (1) |
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126 | (2) |
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Landau Criterion for Superfluidity |
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128 | (1) |
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Normal and Superfluid Densities |
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129 | (2) |
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131 | (5) |
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Gross-Pitaevskii Equation |
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131 | (1) |
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132 | (2) |
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Connection with Fluid Mechanics |
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134 | (2) |
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136 | (7) |
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136 | (1) |
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137 | (3) |
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140 | (3) |
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143 | (15) |
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Quantum Mechanics of a Particle |
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143 | (5) |
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143 | (3) |
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146 | (2) |
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Gauge Invariance and Operator Ordering |
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148 | (2) |
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150 | (2) |
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152 | (1) |
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Gaussian Integrals and Free Fields |
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153 | (3) |
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153 | (2) |
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155 | (1) |
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156 | (2) |
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158 | (13) |
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158 | (8) |
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161 | (5) |
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166 | (5) |
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167 | (4) |
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Path Integrals for Fermions |
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171 | (14) |
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171 | (6) |
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174 | (3) |
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Fermionic Coherent States |
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177 | (2) |
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179 | (6) |
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181 | (4) |
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185 | (16) |
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185 | (4) |
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189 | (2) |
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Interactions and Bose Condensation |
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191 | (4) |
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192 | (3) |
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195 | (6) |
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No Chiral Lattice Fermions |
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200 | (1) |
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The Renormalization Group |
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201 | (12) |
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202 | (4) |
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204 | (1) |
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Two-Dimensional Ising Model |
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205 | (1) |
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Block Spins and Renormalization Group |
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206 | (7) |
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212 | (1) |
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Fields and Renormalization |
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213 | (20) |
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The Free-Field Fixed Point |
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213 | (2) |
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215 | (4) |
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219 | (1) |
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220 | (9) |
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225 | (3) |
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228 | (1) |
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229 | (4) |
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233 | (13) |
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233 | (4) |
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237 | (9) |
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Linear vs. Nonlinear σ-Models |
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241 | (5) |
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A Relativistic State Normalization |
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246 | (2) |
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248 | (2) |
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C Dimensional Regularization |
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250 | (4) |
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C.1 Analytic Continuation and Integrals |
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250 | (2) |
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252 | (2) |
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D Spinors and the Principle of the Sextant |
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254 | (4) |
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D.1 Constructing the γ-Matrices |
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254 | (1) |
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255 | (1) |
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256 | (1) |
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D.4 Spin(2N), Pin(2N), and SU(N) ⊂ SO(2N) |
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257 | (1) |
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258 | (3) |
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261 | (3) |
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G Determinants in Quantum Mechanics |
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264 | (3) |
Index |
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267 | |