  The lifelong efforts of Paul A. M. Dirac were to construct localized quantum
systems in the Lorentz covariant world. In 1927, he noted that the time-energy
uncertainty should be included in the Lorentz-covariant picture. In 1945, he
attempted to construct a representation of the Lorentz group using a
normalizable Gaussian function localized both in the space and time variables.
In 1949, he introduced his instant form to exclude time-like oscillations. He
also introduced the light-cone coordinate system for Lorentz boosts. Also in
1949, he stated the Lie algebra of the inhomogeneous Lorentz group can serve as
the uncertainty relations in the Lorentz-covariant world. It is possible to
integrate these three papers to produce the harmonic oscillator wave function
which can be Lorentz-transformed. In addition, Dirac, in 1963, considered two
coupled oscillators to derive the Lie algebra for the generators of the
$O(3,\,2)$ de Sitter group, which has ten generators. It is proven possible to
contract this group to the inhomogeneous Lorentz group with ten generators,
which constitute the fundamental symmetry of quantum mechanics in Einstein's
Lorentz-covariant world.

Quantum Physics