EFFECTIVE FIELD THEORIES FOR VECTOR PARTICLES AND ...

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Andreas Neiser: Effective Field Theories for Vector Particles and Constraint Analysis, Diplomarbeit erstgutachter: Prof. Dr. Stefan Scherer zweitgutachter: Prof. Dr. Martin Reuter
CONTENTS i introduction and theoretical foundations 1 1 motivation and overview 3 2 qcd and chiral effective field theory 9 2.1 Quantum Chromodynamics . . . . . . . . . . . . . . . . . 9 2.2 Chiral Effective Field Theory . . . . . . . . . . . . . . . . 12 2.3 Inclusion of Vector Mesons . . . . . . . . . . . . . . . . . 17 3 power counting and regularization 21 3.1 Power Counting with Vector Mesons . . . . . . . . . . . . 21 3.2 Reformulated Infrared Regularization . . . . . . . . . . . 23 4 classical constraint analysis 27 4.1 Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . 27 4.2 The Free Tensor Model . . . . . . . . . . . . . . . . . . . . 30 ii applications and calculations 35 5 su(3)-invariant general lagrangian 37 6 vector particles in the tensor model 43 6.1 Available Lorentz Structures . . . . . . . . . . . . . . . . . 43 6.2 Requirement of the U(1) Invariance . . . . . . . . . . . . 46 6.3 Constraint Analysis . . . . . . . . . . . . . . . . . . . . . . 50 6.4 Quantization with Constraints . . . . . . . . . . . . . . . 54 6.5 Naïve Feynman Rules . . . . . . . . . . . . . . . . . . . . . 57 6.6 Renormalizability Analysis . . . . . . . . . . . . . . . . . . 63 6.7 Consistency Check with SU(2) . . . . . . . . . . . . . . . 67 7 magnetic moment of the rho meson 71 7.1 Model Definition and Preliminary Remarks . . . . . . . 72 7.2 Power Counting . . . . . . . . . . . . . . . . . . . . . . . . 73 7.3 Two-Point Function . . . . . . . . . . . . . . . . . . . . . . 75 7.4 Magnetic Moment . . . . . . . . . . . . . . . . . . . . . . . 76 7.5 Reformulated Infrared Regularization . . . . . . . . . . . 82 7.6 Discussion of Results . . . . . . . . . . . . . . . . . . . . . 87 8 summary and conclusion 89 iii
Page 1: EFFECTIVE FIELD THEORIES FOR VECTOR
Page 5: LIST OF FIGURES Figure 4.1 Constrai
Page 9 and 10: The main motivation for working in
Page 11 and 12: motivation and overview 5 in the tr
Page 13: motivation and overview 7 include v
Page 16 and 17: 10 qcd and chiral effective field t
Page 27 and 28: 3 POWER COUNTING AND REGULARIZATION
Page 29 and 30: 3.2 reformulated infrared regulariz
Page 31: 3.2 reformulated infrared regulariz
Page 34 and 35: 28 classical constraint analysis sy
Page 36 and 37: 30 classical constraint analysis 4.
Page 38 and 39: 32 classical constraint analysis Ne
Page 40 and 41: 34 classical constraint analysis wi
Page 43 and 44: 5 SU(3)-INVARIANT GENERAL LAGRANGIA
Page 45 and 46: su(3)-invariant general lagrangian
Page 47: su(3)-invariant general lagrangian
Page 50 and 51: 44 vector particles in the tensor m
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46 vector particles in the tensor m
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7 MAGNETIC MOMENT OF THE RHO MESON
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7.2 power counting 73 which transfo
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7.3 two-point function 75 π c ρ c
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7.4 magnetic moment 77 γ γ ρ 3
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7.4 magnetic moment 79 γ γ γ π
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7.4 magnetic moment 81 This result
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7.5 reformulated infrared regulariz
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7.5 reformulated infrared regulariz
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7.6 discussion of results 87 Method
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SUMMARY AND CONCLUSION 8 This chapt
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summary and conclusion 91 cross-che
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NOTATIONS AND RELATIONS A In this c
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A.2 one-loop integrals 97 The two-p
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TECHNICAL DETAILS B This chapter gi
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B.2 constraint analysis in form 101
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B.2 constraint analysis in form 103
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106 magnetic moment in detail π a
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108 magnetic moment in detail c.2 f
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110 magnetic moment in detail c.3
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112 magnetic moment in detail c.4 n
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114 magnetic moment in detail Diagr
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116 magnetic moment in detail Diagr
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118 bibliography [18] M. R. Schindl
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120 bibliography [56] J. Wess and B
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122 bibliography [95] F. Cardarelli
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