QUANTUM MECHANICS: MATHEMATICS AND IDEAS

Summary

Dirac transformation theory, which is already ninety-one years old, provides a somewhat definitive formulation of quantum mechanics. Indeterminacy, superposition, non-locality, and the intrinsically probabilistic content of the theory have already left generations of physicists with a sense of uneasiness when trying to understand how think of a well-defined macro-world within the conceptual framework of quantum mechanics.

A number of alternative mathematical formulations have followed the one of Dirac [2]. In particular, the phase space formulation of quantum mechanics [3,4] tames some of the problems mentioned above. However, since mathematical equivalence does not imply physical equivalence, one should have to understand the true meaning of the perspective provided by the phase space formulation of quantum mechanics.

From such a point of view, the Principle of the Symplectic Camel [5], i.e., the impossibility of squeezing, by means of classical Hamiltonian dynamics, a phase space volume through a hole in a plane of conjugate coordinates, when the area of the hole is smaller than the cross section of the volume, shows unquestionably that there are imprints of quantum mechanics in the classical formalism. The

consequences of the Symplectic Camel must fully percolate in the physics community yet.
This workshop aims at joining together the communities of mathematicians and physicists in order to discuss both practical calculation problems and matters of principle within different the formulations of quantum mechanics. In particular, a common language to the two communities will also be searched in order to establish a fruitful communication channel for the future.

References

[1] P.A.M. Dirac, "The Physical Interpretation of the Quantum Dynamics", Proceedings of the Royal Society of London. A. 113, 621 (1927).

[2] D. F. Styer, M. S. Balkin, K. M. Becker, M. R. Burns, C. E. Dudley, S. T. Forth, J. S. Gaumer, M. A. Kramer, D. C. Oertel, L. H. Park, M. T. Rinkoski, C. T. Smith, and T. D. Wotherspoon, "Nine formulations of quantum mechanics", American Journal of Physics 70, 288 (2002).

[3] E. P. Wigner, "On the quantum correction for thermodynamic equilibrium," Physical Review 40, 749 (1932).

[4] M. Hillery, R. F. O’Connell , M. O. Scully, and E. P. Wigner, "Distribution Functions in Physics: Fundamentals", Physics Reports 106, 121 (1984).

[5] Maurice A. de Gosson, "The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?", Foundations of Physics 39, 194 (2009). 

 


Speakers

  • Prof. Maurice de Gosson (UniVIE)Prof. Francesco Oliveri
  • Prof. Fabio Bagarello
  • Prof Santi Prestipino (MIFT) Prof. Alessandro Sergi
  • Dr. Francesco Gargano
  • Dr. Grimaudo (UniPA) 

Organizers

  • Prof. Francesco Oliveri (MIFT UniME)
  • Prof. Fabio Bagarello (DEIM UniPA)
  • Prof. Alessandro Sergi (MIFT UniME)
  • Dr. Francesco Gargano (DEIM UniPA)
  • Dr. Matteo Gorgone (MIFT UniME)
  • Andrea Grimaldi (MIFT UniME)
  • Fabio Risitano (MIFT UniME) 

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