Remarks on the Theorems of Inconsistency of Heisenberg Lie Symplectic Formulations

Ruggero María Santilli

A number of problematic aspects of conventional quantum mechanical formulations have been recently focused. A few rudimentary remarks are presented in the hope of contributing toward a more adequate identification of the open problems, as a prerequisite for their future resolution.

F. Bayen, J. M. Maillard

R. G. G. Amorim, S. C. Ulhoa, Edilberto O. Silva

Guillermo Chacón‐Acosta, Angel García-Chung

In this paper, we show the relation between $sp(4,\mathbb{R})$, the Lie algebra of the symplectic group, and the elements of $Sp(4,\mathbb{R})$. We use this result to obtain some special cases of symplectic matrices relevant to the study of squeezed states. In this regard, we provide some applications in quantum mechanics and analyze the squeezed polymer states obtained from the polymer representation of the symplectic group. Remarkably, the polymer's dispersions are the same as those obtained for the squeezed states in the usual representation.

D. J. Simms, L. Castel

Guido Bacciagaluppi

At the 1927 Solvay conference Born and Heisenberg presented a joint report on quantum mechanics. I suggest that the significance of this report lies in that it contains a ‘final’ formulation of the statistical interpretation of quantum mechanics that goes beyond Born’s origi-nal proposal. In particular, this formulation imports elements from Heisenberg’s work as well as from the transformation theory of Dirac and Jordan. I suggest further a reading of Born and Heisenberg’s position in which the wave function is an effective notion. This can make sense of a remarkable aspect of their presentation, namely the fact that the ‘quantum mechanics’ of Born and Heisenberg apparently lacks wave function collapse.