Overview

One of the most fruitful and still promising approaches to unifying quantum mechanics and special relativity has been the covariant formulation of quantum field theory. An important starting point is Wigner’s 1939 paper and the physical ideas presented in his 1931 book. This early work was overshadowed by the success of quantum field theory until the 1950s. However, with the discovery of the extended charge distribution of protons leading to the quark theory for all hadrons, the difficulties with using quantum field theory for quarks confined in bound states became apparent along with the difficulties of reconciling quantum mechanics with special relativity. Paul A. M. Dirac devoted much of his professional life to this important task. In his attempt to construct a relativistic dynamics of atom contained in his 1949 article, Dirac emphasizes that the task of constructing a relativistic dynamics is equivalent to constructing a representation of the Poincaré group, also known as the inhomogeneous Lorentz group. In the 1950s, the limitations of the present form of quantum field theory became apparent. Currently, there are two different opinions on the difficulty of using field theory in dealing with bound-state problems or systems of confined quarks.