Elaboration of the recently proposed test of Pauli's principle under strong interactions

The primary objective of this paper is to stimulate the experimental verification of the validity or invalidity of Pauli's principle under strong interactions, according to a proposal which has recently appeared in the literature. For this objective, we first outline the most relevant steps in the evolution of the notion of particle, from the classical notion of massive point, to the quantum-mechanical notion of massive, spinning, and charged particle under electromagnetic interactions, as characterized by the Poincar\'e symmetry and as experimentally established. We then recall recent studies according to which this latter notion of particle might still need suitable implementations when referred to the additional presence of strong interactions. By recalling that no experimental evidence of direct, or final or unequivocal character is available at this moment on the value of the spin under strong interactions, the following hypothesis of these studies is recalled. It consists of the idea that the spin as well as other intrinsic characteristics of extended, massive, particles under electromagnetic interactions at large distances are subjected to a mutation under additional strong interactions at distances smaller than their charge radius. These dynamical effects can apparently be conjectured to account for the nonpointlike nature of the particles, their necessary state of penetration to activate the strong interactions, and the consequential emergence of broader forces which imply the breaking of the SU(2)-spin symmetry. Among the rather numerous technical problems which must be studied to reach a quantitative assessment of these ideas, in this paper we study a characterization of the mutated value of the spin via the transition from the associative enveloping algebra of SU(2) to a nonassociative Lie-admissible form. The departure from the original associative product then becomes directly representative of the breaking of the SU(2)-spin symmetry, the presence of forces more general than those derivable from a potential, and the mutated value of the spin. In turn, such a departure of the spin from conventional quantum-mechanical values implies the inapplicability of Pauli's exclusion principle under strong interactions, because, according to this hypothesis, particles that are fermions under long-range electromagnetic interactions are no longer fermions under these broader, short-range, forces. The case of nuclear physics is considered in detail. It is stressed that, in this case, possible deviations from Pauli's exclusion principle can at most be very small. A class of nuclei for the test considered is selected. It consists of all nuclei whose volume lies below the value predicted by the proportionality law of the nuclear volume with the total number of nucleons. These experimental data establish that, for the nuclei considered, nucleons are in a partial state of penetration of their charge volumes although of small statistical character. In turn, this state of penetration of the charge volumes activates the model of breaking of the SU(2)-spin symmetry reviewed in this paper.