Quantum Field Theory II: Quantum Electrodynamics: A Bridge between Mathematicians and PhysicistsAnd God said, Let there be light; and there was light. Genesis 1,3 Light is not only the basis of our biological existence, but also an essential source of our knowledge about the physical laws of nature, ranging from the seventeenth century geometrical optics up to the twentieth century theory of general relativity and quantum electrodynamics. Folklore Don’t give us numbers: give us insight! A contemporary natural scientist to a mathematician The present book is the second volume of a comprehensive introduction to themathematicalandphysicalaspectsofmodernquantum?eldtheorywhich comprehends the following six volumes: Volume I: Basics in Mathematics and Physics Volume II: Quantum Electrodynamics Volume III: Gauge Theory Volume IV: Quantum Mathematics Volume V: The Physics of the Standard Model Volume VI: Quantum Gravitation and String Theory. It is our goal to build a bridge between mathematicians and physicists based on the challenging question about the fundamental forces in • macrocosmos (the universe) and • microcosmos (the world of elementary particles). The six volumes address a broad audience of readers, including both und- graduate and graduate students, as well as experienced scientists who want to become familiar with quantum ?eld theory, which is a fascinating topic in modern mathematics and physics. |
Contents
Part II Basic Ideas in Classical Mechanics | 263 |
Part III Basic Ideas in Quantum Mechanics | 426 |
Part IV Quantum Electrodynamics QED | 771 |
Part V Renormalization | 945 |
Common terms and phrases
bosonic bundle C*-algebra calculus called classical complex numbers compute consider convergent corresponds define definition denotes differential equations Dirac electron elements energy equivalent example exists Explicitly fermionic Feynman diagrams Feynman propagator finite formal formula Fourier transform function f gauge Gaussian geometry given Green's function Hamiltonian harmonic oscillator Heisenberg Hence Hfree Hilbert space Hopf algebra interval introduce Lagrangian linear space manifold Math mathematics matrix method momentum morphism motion obtain orthonormal parameter path integral perturbation photon Phys physicists physics problem proof propagator kernel quantization quantum electrodynamics quantum field theory quantum mechanics quantum particle real line real numbers relation renormalization resp S-matrix scattering Schrödinger equation Sect self-adjoint operator smooth solution Springer subset symmetry symplectic tangent tempered distributions theorem topological space vector wave Weyl York