This book introduces notation, terminology, and basic ideas of relativistic quantum theories. The discussion proceeds systematically from the principle of relativity and postulates of quantum logics to the construction of Poincare invariant few-particle models of interaction and scattering. It is the first of three volumes formulating a consistent relativistic quantum theory of interacting charged particles. Contents Quantum logic Poincare group Quantum mechanics and relativity Observables Elementary particles Interaction Scattering Delta function Groups and vector spaces Group of rotations Lie groups and Lie algebras Hilbert space Operators Subspaces and projections Representations of groups and algebras Pseudo-orthogonal representation of Lorentz group

This second volume of three on relativistic quantum theories of interacting charged particles discusses quantum theories of systems with variable numbers of particles. Basics of the Fock space and quantum electrodynamics are covered with an emphasis on renormalization. In contrast to the usual treatment of the topic, particles (rather than fields) are chosen as basic ingredients. Contents Fock space Scattering in Fock space Quantum electrodynamics Renormalization Useful integrals Quantum fields of fermions Quantum field of photons QED interaction in terms of particle operators Relativistic invariance of QFT Loop integrals in QED Scattering matrix in (v/c)2 approximation Checks of physical dimensions

In this third volume of three, quantum electrodynamics is formulated in the language of physical "dressed" particles. A theory where charged particles interact via instantaneous action-at-a-distance forces is constructed - without need for renormalization. This theory describes electromagnetic phenomena in terms of directly interacting charges, but in full accord with fundamental principles of relativity and causality. Contents Three ways to look at QFT Dressing What are advantages of dressed Hamiltonian? Coulomb potential and beyond Decays RQD in higher orders Classical electrodynamics Experimental support of RQD Particles and relativity Special theory of relativity Unitary dressing transformation Integral for decay law Coulomb scattering integral in fourth order Relativistic invariance of Coulomb-Darwin-Breit electrodynamics