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1 | (3) |
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2 Quark bilinear operators |
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4 | (6) |
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2.1 Lorentz transformations of qXXXq bilinear operators |
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4 | (1) |
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2.2 Isospin and flavor rotations |
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4 | (2) |
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2.3 Right and left rotations |
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6 | (1) |
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2.4 Quantum numbers of qXXXq operators |
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7 | (1) |
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2.5 Diquark bilinear operators |
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8 | (2) |
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3 Effective quark interactions |
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10 | (10) |
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3.1 Gluon exchange interactions |
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10 | (4) |
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3.1.1 Gluon exchange in the colorless qq channel |
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11 | (2) |
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3.1.2 Gluon exchange in the diquark channel |
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13 | (1) |
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3.2 Instanton induced quark interactions |
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14 | (3) |
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3.3 Comparison between interactions |
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17 | (1) |
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3.4 Non-local effective interactions |
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17 | (3) |
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4 The Nambu Jona-Lasinio model |
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20 | (14) |
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4.1 The lagrangian and the hamiltonian of the Nambu Jona-Lasinio model |
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20 | (1) |
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4.2 The partition function and the euclidean action. |
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21 | (1) |
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4.3 Bosonization of the euclidean action |
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22 | (4) |
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4.4 Three equivalent descriptions of the system |
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26 | (1) |
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4.5 Symmetries of the Nambu Jona-Lasinio model |
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27 | (4) |
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28 | (1) |
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29 | (1) |
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30 | (1) |
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4.6 The case of large quark masses |
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31 | (3) |
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4.6.1 Suppression of the SU (N(f)) generators |
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31 | (1) |
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4.6.2 Heavy quark spin symmetry |
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32 | (2) |
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5 The equivalent linear sigma model |
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34 | (16) |
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5.1 The Nambu Jona-Lasinio action with scalar fields |
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34 | (2) |
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36 | (2) |
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5.3 The large N(c) limit and caveats thereon |
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38 | (1) |
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5.4 The equivalent linear sigma model in a simplified SU (2) (f) case |
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39 | (2) |
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5.5 Setting the scale by fitting f(XXX) |
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41 | (3) |
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5.6 SU (3)(f) scalar fields |
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44 | (6) |
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5.6.1 The pseudoscalar XXX, K, XXX nonet (L = O, J(P) = O(-)) |
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45 | (2) |
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5.6.2 The scalar a(o), K(*), f(o) nonet (L = 1, J(P) = O(+)) |
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47 | (3) |
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50 | (10) |
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6.1 Non-local regularizations |
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51 | (4) |
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6.1.1 Regularization by delocalized fields |
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51 | (2) |
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6.1.2 Quarks which cannot materialize on-shell |
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53 | (2) |
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55 | (1) |
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6.3 Regularizations of the real part |
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56 | (4) |
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6.3.1 Proper-time regularization |
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57 | (1) |
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6.3.2 Pauli-Villars regularization |
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58 | (2) |
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7 Correlation functions: basic properties |
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60 | (12) |
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7.1 Spectral decomposition of correlation functions |
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60 | (2) |
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7.2 The interpretation of poles in the complex q(2) plane |
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62 | (3) |
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7.2.1 Poles on the negative real axis: on-shell particles |
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62 | (1) |
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7.2.2 Poles on the Positive real axis: Landau ghosts |
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63 | (1) |
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7.2.3 Poles in the complex q(2) plane |
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64 | (1) |
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65 | (1) |
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7.4 The generating functional and the effective action |
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66 | (4) |
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7.4.1 Definition of the effective action |
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67 | (1) |
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7.4.2 Properties of the effective action |
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67 | (1) |
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7.4.3 The effective action XXX in the one-loop approximation |
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68 | (2) |
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7.5 The generating functional of quark bilinear forms |
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70 | (2) |
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8 Symmetry conserving approximations |
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72 | (15) |
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8.1 A generic form of the action |
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72 | (1) |
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73 | (3) |
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8.2.1 Unlabeled Feynman graphs for the generating functional |
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73 | (2) |
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8.2.2 Labeled Feynman graphs for correlation functions of the fields |
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75 | (1) |
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8.2.3 Labeled Feynman graphs for correlation functions of quark bilinear operators |
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75 | (1) |
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8.3 The Feynman graph expansion of the effective action |
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76 | (3) |
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8.4 The symmetry conserving property |
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79 | (1) |
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8.5 The leading order contribution in N(c) |
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80 | (1) |
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8.6 Next to leading order contribution in N(c) |
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81 | (1) |
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8.7 Self-consistent Schwinger-Dyson and Bethe-Salpeter equations |
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82 | (5) |
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9 Correlation functions in the Nambu Jona-Lasinio model |
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87 | (16) |
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9.1 Second order expansion of the action |
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87 | (2) |
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9.2 Meson propagators in the scalar channels |
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89 | (5) |
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9.2.1 Correlation functions of the pseudoscalar nonet |
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91 | (1) |
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9.2.2 The decay constants f(XXX) and f(K) |
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92 | (1) |
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9.2.3 The quark condensates |
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93 | (1) |
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9.2.4 Correlation functions of the scalar nonet |
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93 | (1) |
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9.3 Vector meson propagators |
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94 | (5) |
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9.3.1 Expansion of the action in powers of the vector fields |
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94 | (3) |
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9.3.2 The p(770) and w(782) propagators |
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97 | (1) |
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9.3.3 The pion propagator and f(XXX) |
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97 | (1) |
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9.3.4 The unbound a(1) (1235) meson and the dangers of gradient expansions |
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98 | (1) |
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9.4 Electromagnetic gauge fields in non-local models |
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99 | (3) |
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9.5 Electroweak fields in regularized models |
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102 | (1) |
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10 Overview of results in the meson sector |
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103 | (20) |
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10.1 The model parameters and fits to the pseudoscalar nonet |
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103 | (3) |
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10.2 Chiral perturbation theory |
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106 | (1) |
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10.3 Radiative decays of pseudoscalar and vector mesons |
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107 | (1) |
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10.4 Restoration of chiral symmetry at finite baryonic density |
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108 | (6) |
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10.4.1 Simple model of spontaneous chiral symmetry breaking |
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108 | (1) |
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10.4.2 Quarks or nucleons in the Fermi sea? |
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109 | (3) |
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10.4.3 Mesons propagating in a dense medium |
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112 | (2) |
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10.5 Systems at finite temperature |
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114 | (9) |
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10.5.1 The mathematical tool |
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115 | (3) |
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10.5.2 The physical content |
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118 | (2) |
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10.5.3 Restoration of chiral symmetry at high temperatures |
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120 | (3) |
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11 Further chiral quark models |
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123 | (11) |
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11.1 The Diakonov Petrov model. |
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123 | (1) |
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11.2 Scaled models involving a dilation field |
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124 | (3) |
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11.3 The Gell-Mann Levy model |
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127 | (5) |
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11.3.1 The action of the model |
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128 | (1) |
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11.3.2 Comparison of the Gell-Mann Levy and the Nambu Jona-Lasinio models |
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128 | (2) |
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130 | (2) |
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11.4 Quark confinement in color dielectric models |
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132 | (2) |
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134 | (21) |
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12.1 u and d quarks interacting with a hedgehog field |
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135 | (4) |
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12.2 Skyrme's topological density |
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139 | (3) |
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12.3 The soliton calculated with proper-time regularization |
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142 | (2) |
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12.4 Hermitian and antihermitian probes |
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144 | (3) |
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12.5 The baryon number and valence orbits |
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147 | (2) |
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12.6 Self-consistent symmetries of SU (3)(f) solitons |
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149 | (2) |
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12.7 Spontaneously broken symmetries |
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151 | (1) |
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12.8 SU (2)(f) solitons in the proper-time regularized Diakonov Petrov model |
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151 | (1) |
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12.9 Problems with soliton stability |
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152 | (1) |
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12.10 A problem related to vector interactions |
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153 | (2) |
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13 Rotations of solitons in flavor space |
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155 | (17) |
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13.1 Introduction of collective coordinates |
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156 | (1) |
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13.2 Rotations of a hedgehog soliton |
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157 | (2) |
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13.3 SU (2)(f) rotations of a G = O soliton |
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159 | (4) |
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13.4 The coupling of operators to the rotating soliton |
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163 | (3) |
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13.5 Calculated nucleon properties |
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166 | (1) |
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13.6 SU (3)(f) rotations of the G = O soliton |
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166 | (3) |
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13.7 Calculated properties of the N (939) octet |
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169 | (3) |
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A SU (N) matrices, Dirac matrices, Fierz transformations |
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172 | (6) |
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A.1 Properties of SU (N) matrices |
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172 | (3) |
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A.1.1 Fierz transformations of products of SU (N) matrices |
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173 | (2) |
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175 | (1) |
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A.3 Fierz transformations of Dirac matrices. |
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176 | (2) |
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178 | (12) |
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B.1 The hamiltonian and the intrinsic generators |
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178 | (3) |
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B.2 Intrinsic and lab frame generators |
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181 | (1) |
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B.3 The partition function |
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182 | (1) |
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183 | (2) |
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185 | (5) |
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190 | (2) |
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C.1 Gaussian transformations and Wick theorems |
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190 | (2) |
| References |
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192 | (9) |
| Index |
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201 | |
