## Field QuantizationTheoretical physics has become a many-faceted science. For the young stu dent it is difficult enough to cope with the overwhelming amount of new scientific material that has to be learned, let alone obtain an overview of the entire field, which ranges from mechanics through electrodynamics, quantum mechanics, field theory, nuclear and heavy-ion science, statistical mechanics, thermodynamics, and solid-state theory to elementary-particle physics. And this knowledge should be acquired in just 8-10 semesters, during which, in addition, a Diploma or Master's thesis has to be worked on or examinations prepared for. All this can be achieved only if the university teachers help to introduce the student to the new disciplines as early on as possible, in order to create interest and excitement that in turn set free essential new energy. At the Johann Wolfgang Goethe University in Frankfurt we therefore con front the student with theoretical physics immediately, in the first semester. Theoretical Mechanics I and II, Electrodynamics, and Quantum Mechanics I - An Introduction are the basic courses during the first two years. These lectures are supplemented with many mathematical explanations and much support material. After the fourth semester of studies, graduate work begins, and Quantum Mechanics II - Symmetries, Statistical Mechanics and Ther modynamics, Relativistic Quantum Mechanics, Quantum Electrodynamics, the Gauge Theory of Weak Interactions, and Quantum Chromo dynamics are obligatory. |

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### Contents

Classical Field Theory | 31 |

3 | 56 |

The KleinGordon Equation | 75 |

The Dirac Equation | 117 |

The Maxwell and Proca Equations | 141 |

Quantization of the Photon Field | 171 |

Interacting Quantum Fields | 211 |

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### Common terms and phrases

AF(a amplitude angular-momentum annihilation operators anticommutation antiparticle boson calculation charge conjugation classical coefficients commutation relations condition conjugate field constructed contains contribution coordinates creation and annihilation defined delta function depend described differential Dirac field eigenstates eigenvalues energy equation of motion euclidian evaluate Example Exercise expansion expectation value fermion Feynman propagator field operator Fourier functional derivative gauge Gaussian integral Grassmann variables Green's function Hamiltonian Heisenberg Heisenberg picture hermitean interaction invariant Klein–Gordon field Lagrange density Lagrangian leads Lorentz matrix element momentum space n-point functions normalization obtained parity path integral phase factor photon plane waves properties quantization quantum field theory quantum mechanics result satisfies scalar field Sect ſº spin spinors symmetry tensor theorem time-ordered product vacuum vacuum expectation value vanishes vector field wave function Woſ.J