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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 scalar propagators are Green's functions for the Klein–Gordon equation. There are related singular functions which are important in quantum field theory. These functions are most simply defined in terms of the vacuum expectation value of products of field operators.
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.
1.3 The Klein–Gordon and Dirac equations for free ... The classical Hamiltonian for a particle in a potential is the kinetic ... the solution to the KG equation.
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.
Moreover, the free fields operators, i.e. when interactions are assumed not to exist, turn out to (formally) satisfy the same equation as do the fields (wave functions) in many cases. Thus the Klein–Gordon equation (spin 0) and the Dirac equation (spin 1 ⁄ 2) in this guise remain in the theory.
The Klein–Gordon equation is ... it is possible to express it through an infinite perturbation series of the free two ... Supersymmetry is a potential solution to ...