Seminar @ DF-TS - Tue Jun 12th 2:30 pm - M. Oppio

[Rosita Glavina - Dip. Fisica UniTS]

We are pleased to announce the seminar @ DF-Theory Section UniTs:
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Marco Oppio
University of Trento

"Quantum theory in real or quaternionic Hilbert spaces: how the complex 
Hilbert space structure emerges from Poincaré symmetry"

Tuesday, June 12th 2018 - 2:30 pm
Room 204, Leonardo Building, Strada Costiera, 11

ABSTRACT
In principle, the lattice of elementary propositions of a generic 
quantum system admits a representation in real, complex or quaternionic 
Hilbert spaces as established by Solèr’s theorem (1995) closing a 
long-standing problem that can be traced back to the von Neumann’s 
mathematical formulation of quantum mechanics. Some remarkable attemps 
have been made in the years to justify such a privileged role of the 
complex numbers, even though a mathematically rigorous analysis in the 
more general case of relativistic systems is still abstent to our 
knowledge. The strategy has always been the same: construct some 
suitable complex structure which commutes with all the observables. Such 
an object allows for a complexification of the Hilbert space. Adopting a 
similar strategy, we show that elementary relativistic systems cannot be 
described in real or quaternionic Hilbert spaces as a consequence of 
some peculiarity of the continuous unitary representations of the 
(universal covering of the) proper orthochronous Poincaré group related 
with the theory of polar decomposition of operators. Indeed any such 
attempt leads necessarily to an equivalent formulation in terms of a 
suitable complex Hilbert space.

The flyer can be downloaded at
http://df.units.it/sites/df.units.it/files/Locandina%20Oppio.pdf

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The calendar of events taking place at the Physics Department is 
available at
https://df.units.it/en/events/all_evnt/