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Physics  2000 

The Klein-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 $\h$. 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 $\h\to 0$, these phenomena disappear. However, in dimension 2 or 3, when $\h\to 0$, the creation probability of particle-antiparticle pairs is not zero.


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