Why don't we formulate quantum theories in real Hilbert spaces? (Part II)

Luogo:  Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari "-1"
Ore 15:00

• Relatore: Marco Oppio (Università di Trento)

Abstract:
As shown in the previous seminar, a "naive" attempt to define a relativistic particle on a real Hilbert space by borrowing the well-known approach of Wigner leads necessarily to an equivalent formulation on a complex Hilbert space. Although this conclusion seems to give a definitive answer to the real-quantum-mechanics issue, it lacks consistency since it does not derive from more general physical hypotheses as the complex one does.
Trying a more solid approach we end up with three possibilities: an equivalent description in terms of Wigner unitary representations on a real, complex or quaternionic Hilbert space. At this point the "naive" result turns out to be a definitely important technical lemma, for it forbids the extreme options. Conclusion, the real theory is actually complex

Referente: Davide Pastorello