Principle of minimum distance in space of states as new principle in quantum physics

The mathematician Leonhard Euler (1707-1783) appears to have been a philosophical optimist having written: "Since the fabric of universe is the most perfect and is the work of the most wise Creator, nothing whatsoever take place in this universe in which some relation of maximum or minimum does not appear. Wherefore, there is absolutely no doubt that every effect in universe can be explained as satisfactory from final causes themselves the aid of the method of Maxima and Minima, as can from the effective causes". Having in mind this kind of optimism in the papers [1-16] we introduced and investigated the possibility to construct a predictive analytic theory of the elementary particle interaction based on the principle of minimum distance in the space of quantum states (PMD-SQS). So, choosing the partial transition amplitudes as the system variational variables and the distance in the space of the quantum states as a measure of the system effectiveness, we obtained the results [1-16]. These results proved that the principle of minimum distance in space of quantum states (PMD-SQS) can be chosen as variational principle by which we can find the analytic expressions of the partial transition amplitudes. In this paper we present a description of hadron-hadron scattering via principle of minimum distance PMD-SQS when the distance in space of states is minimized with two directional constraints: d sigma/d Omega(+/- 1) =fixed. Then by using the available experimental (pion-nucleon and kaon-nucleon) phase shifts we obtained not only consistent experimental tests of the PMD-SQS optimality, but also strong experimental evidences for new principles in hadronic physics such as: Principle of nonextensivity conjugation via the Riesz-Thorin relation (1/2p + 1/2q = 1) and a new Principle of limited uncertainty in nonextensive quantum physics. The strong experimental evidence obtained here for the nonextensive statistical behavior of the [J, theta]-quantum states in the pion-nucleon, kaon-nucleon and antikaon-nucleon scatterings can be interpreted as an indirect manifestation the presence of the quarks and gluons as fundamental constituents of the scattering system having the strong-coupling long-range regime required by the Quantum Chromodynamics.