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. |
Contents
Classical and Quantum Mechanics of Particle Systems | 3 |
The Maxwell and Proca Equations | 6 |
Classical Field Theory | 31 |
Nonrelativistic Quantum Field Theory 57 | 56 |
The KleinGordon Equation | 75 |
141 | 110 |
The Dirac Equation | 117 |
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Common terms and phrases
angular-momentum annihilation operators anticommutation antiparticles boson canonical coefficients commutation relations condition conjugate field contains contribution coordinates creation and annihilation d³p d³x defined delta function dependence differential Dirac Dirac field eigenstates energy equation of motion euclidian evaluate Example Exercise expansion expectation value factor fď³x fermion Feynman propagator field operator Fourier functional derivative gauge Gaussian integral graphs Grassmann Grassmann variables Green's function Hamiltonian Heisenberg picture interaction invariant Klein-Gordon equation Lagrange density Lagrangian leads Lorentz matrix element momentum space normalization obtained operators â particles path integral perturbation photon plane waves Poisson brackets quantization quantum mechanics result satisfy Schrödinger Sect spinors symmetry tensor theorem transformation up(x vacuum vacuum expectation value vanish variables vector wave function Wo[J ас әс