Relativistic Quantum Mechanics and Introduction to Field Theory

A fully relativistic treatment of the quantum mechanics of particles requires the introduction of quantum field theory, that is to say, the quantum mechan- ics of systems with an infinite number of degrees of freedom. This is because the relativistic equivalence of mass and energy plus the quantum possibility of fluctuations imply the existence of (real or virtual) creation and annihilation of particles in unlimited numbers. In spite of this, there exist processes, and energy ranges, where a treat- ment in terms of ordinary quantum mechanical tools is appropriate, and the approximation of neglecting the full field-theoretic description is justified. Thus, one may use concepts such as potentials, and wave equations, clas- sical fields and classical currents, etc. The present text is devoted precisely to the systematic discussion of these topics, to which we have added a gen- eral description of one- and two-particle relativistic states, in particular for scattering processes. A field-theoretic approach may not be entirely avoided, and in fact an introduction to quantum field theory is presented in this text. However, field theory is not the object per se of this book; apart from a few examples, field theory is mainly employed to establish the connection with equivalent potentials, to study the classical limit of the emission of radiation or to discuss the propagation of a fermion in classical electromagnetic fields.