Quantum field theory is the basic tool to understand the physics of the elementary constituents of matter. … It is both a very powerful and a very precise framework: using it we can describe physical processes in a range of energies going from the few millions electrovolts typical of nuclear physics to the thousands of billions of the Large Hadron Collider (LHC). And all this with astonishing precision.
In spite of the impressive success of quantum mechanics in describing atomic physics, it was immediately clear after its formulation that its relativistic extension was not free of difficulties.
If Dirac’s idea restores the stability of the spectrum by introducing a stable vacuum where all negative energy states are occupied, the so-called Dirac sea, it also leads directly to the conclusion that a single-particle interpretation of the Dirac equation is not possible.
In 1929 Oskar Klein stumbled into an apparent paradox when trying to describe the scattering of a relativistic electron by a square potential using Dirac’s wave equation. … In order to capture the essence of the problem without entering into unnecessary complication we will study Klein’s paradox in the context of the Klein– Gordon equation.