Real quantum mechanics in Kaehler space: exact isomorphism with complex quantum theory and maximal Bell-inequality violation
prof. dr hab. Jean-Pierre Gazeau
Chair of Mathematical Physics, 2026-04-24 godz. 9:45 - 11:15
We revisit the role of complex numbers in quantum mechanics and question whether they are fundamental or merely a convenient mathematical representation. A recent result claimed that real formulations of quantum theory can be experimentally ruled out.
We show that this conclusion relies on an incomplete real framework. By introducing a real Hilbert space endowed with a symplectic structure and a compatible complex structure, we construct a formulation that is exactly equivalent to standard complex quantum mechanics. This equivalence extends naturally to composite systems through an alternative composition rule.
Within this setting, we recover the maximal quantum violations in Bell-type scenarios using purely real variables, thereby challenging previous claims. Our results support the view that complex numbers in quantum mechanics reflect an underlying real geometric structure rather than a fundamental ingredient.
English
Polski
Print
