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Any solution of the free Dirac equation is, for each of its four components, a solution of the free Klein–Gordon equation. Despite historically it was invented as a single particle equation the Klein–Gordon equation cannot form the basis of a consistent quantum relativistic one-particle theory, any relativistic theory implies creation and ...
The Klein paradox is an unexpected consequence of relativity on the interaction of quantum particles with electrostatic potentials. The quantum mechanical problem of free particles striking an electrostatic step potential has two solutions when relativity is ignored.
A classical free scalar field satisfies the Klein–Gordon equation. If a scalar field is denoted , a quartic interaction is represented by adding a potential energy term (/!) to the Lagrangian density.
Two solutions of these equations for the same current configuration differ by a solution of the vacuum wave equation = In this form it is clear that the components of the potential separately satisfy the Klein–Gordon equation , and hence that the Lorenz gauge condition allows transversely, longitudinally, and "time-like" polarized waves in ...
The Higgs field φ satisfies the Klein–Gordon equation. The weak interaction fields Z, W ± satisfy the Proca equation. These equations can be solved exactly. One usually does so by considering first solutions that are periodic with some period L along each spatial axis; later taking the limit: L → ∞ will lift this periodicity restriction.
In 1927, Klein, Gordon and Fock also found it, but incorporated the electromagnetic interaction and proved that it was Lorentz invariant. De Broglie also arrived at the same equation in 1928. This relativistic wave equation is now most commonly known as the Klein–Gordon equation. [21]
This is the Klein–Gordon equation, ... known as a double well potential, ... known example of a scalar field theory with kink solutions is the sine-Gordon theory.
where A μ is the electromagnetic four-potential in Lorenz gauge. The Klein–Gordon equation has ... A special solution is given by the retarded Green's function ...