Introduction and some problems encountered in the construction of a relativistic quantum theory

One of the deepest and most difficult problems of theoretical physics in the past century has been the construction of a simple, well-defined one-particle theory which unites the ideas of quantum mechanics and relativity. Early attempts, such as the construction of the Klein-Gordon equation and the Dirac equation were inadequate to provide such a theory since, as shown by Newton and Wigner (1949), they are intrinsically non-local, in the sense that the solutions of these equations cannot provide a well-defined local probability distribution. This result will be discussed in detail below. Relativistic quantum field theories, such as quantum electrodynamics, provide a manifestly covariant framework for important questions such as the Lamb shift and other level shifts, the anomalous moment of the electron and scattering theory, but the discussion of quantum mechanical interference phenomena and associated local manifestations of the quantum theory are not within their scope; the one particle sector of such theories display the same problem pointed out by Newton and Wigner since they satisfy the same one-particle field equations.