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267 pages, year 2005

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Contents highlights: The Dirac Field, The ScatteringMatrix, Feynman diagrams in momentum space, Fermionic oscillators and Grassmann algebras, Path Integrals and non-Abelian gauge theories. Quoted contents: "2 One-loop renormalization p.36 2.1 Divergences of the Feynman integrals 36 2.2 Higher order corrections 38 2.3 The analysis by counterterms p.45 2.4 Dimensional regularization of the Feynman integrals p.52 2.5 Integration in arbitrary dimensions 54 2.6 One loop regularization of QED 56 2.7 One loop renormalization 63 3 Vacuum expectation values and the S matrix 73 3.1 In-- and Out --states p.73 3.2 The S matrix p.79 3.3 The reduction formalism 81 4 Path integral formulation of quantum mechanics 85 4.1 Feynman’s formulation of quantummechanics 85 4.2 Path integral in configuration space 88 .3 The physical interpretation of the path integral 91 4.4 The free particle 97 4.5 The case of a quadratic action p.99 4.6 Functional formalism 104 4.7 General properties of the path integral 107 4.8 The generating functional of the Green’s functions 113 4.9 The Green’s functions for the harmonic oscillator 116 5 The path integral in field theory 123 5.1 The path integral for a free scalar field 123 5.2 The generating functional of the connected Green’s functions 127 5.3 The perturbative expansion for the theory lambda phi4 129 5.4 The Feynman’s rules in momentum space 135 5.5 Power counting in lambda--phi4 137 5.6 Regularization in lambda--phi4 142 5.7 lambda phi4 145 6 The renormalization group 152 6.1 The renormalization group equations 152 6.2 Renormalization conditions 156 6.3 Application to QED 160 6.4 Properties of the renormalization group equations 161 6.5 The coefficients of the renormalization group equations and the renormalization conditions p. 167 7 The path integral for Fermi fields 169 7.1 Fermionic oscillators and Grassmann algebras p.169 7.2 Integration over Grassmann variables p.174 7.3 The path integral for the fermionic theories p.178 8 The quantization of the gauge fields 180 8.1 QED as a gauge theory p.180 8.2 Non-abelian gauge theories p.182 8.3 Path integral quantization of the gauge theories p. 186 8.4 Path integral quantization of QED 196 8.5 Path integral quantization of the non--abelian (non-Abelian) gauge theories p.200 8.6 The beta-function in non-abelian gauge theories 204 9 Spontaneous symmetry breaking 213 9.1 The linear sigma-model p.213 9.2 Spontaneous symmetry breaking p. 219 9.3 The Goldstone theorem p. 223 9.4 The Higgs mechanism 225 9.5 Quantization of a spontaneously broken gauge theory in the Rzeta-gauge 230 9.6 zeta-cancellation in perturbation theory p. 235 10 The Standard model of the electroweak interactions 239 10.1 The StandardModel of the electroweak interactions p. 239 10.2 The Higgs sector in the Standard Model 244 10.3 The electroweak interactions of quarks and the Kobayashi--Maskawa--Cabibbo matrix 249 10.4 The parameters of the SM 258 10.5 Ward identities and anomalies A.1 Properties of the real antisymmetric matrices p. 265." Dowloadable at: http://theory.fi.infn.it/casalbuoni/lezioni99.pdf "Lezioni date all' Universita' di Firenze nell'a.a. 2004/2005."

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open access: http://theory.fi.infn.it/casalbuoni/lezioni99.pdf

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