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The Klein-Gordon's field. A counter-example of the classical limit

Jaume Haro
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Abstract

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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Jaume Haro. 2000-02-22. The Klein-Gordon's field. A counter-example of the classical limit. https://arxiv.org/abs/math-ph/0002042

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