par Van Hove, Léon
Référence Physica, 18, 3, page (145-159)
Publication Publié, 1952-03
Article révisé par les pairs
Résumé : It is well known that for a neutral scalar field in scalar interaction with infinitely heavy, fixed point sources, the stationary states can be determined exactly. This simple case of quantized field is considered for the discussion of the following two problems: to investigate the origin of the divergence difficulties which are unavoidably brought in when the interaction is treated as a perturbation, and to see how good a description of the exact solution is obtained from the perturbation method as improved by the renormalization technique for discarding divergences. The origin of the divergences is found to lie in the fact that the stationary states of the field interacting with the sources are no linear combinations of the stationary states of the free field. The former are not contained in the Hilbert space spanned by the latter (they even turn out to be orthogonal to this space). As a consequence of results obtained in a previous paper, a similar property is shown to hold for the more realistic case of two interacting fields under the mere assumption that stationary states exist in presence of interaction. Regarding the second problem, whereas the exact solution and the results obtained by perturbation and renormalization methods are in agreement for the S matrix, they are found to disagree for the unitary matrix S(t) expressing the change of the wave vector between times t = - ∞ and t finite. © 1952.