The Lein-Gordon's field: a counter-example of the classical limit
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We will study the Klein-Gordon's field with an homogeneous external potential, which does not depend on ħ. We will construct the Fock's space corresponding to our problem and we will see that there are phenomena of creation and anihilation of pairs particle-antiparticle. Finally, we will see that in dimension 1,when ħ→0, these phenomena disappear. However, in dimension 2 or 3, when ħ→0, the creation probability of particle-antiparticle pairs is not zero.