On the properties of real quantum mechanics in Kähler Space

We investigate the isomorphism between the formulations of quantum mechanics in a finite-dimensional complex Hilbert space and in a real Kähler space. This investigation establishes a direct correspondence between Hermitian operators in the complex Hilbert space and real operators in the Kähler space. In this real formulation, we note the emergent property of spectral degeneracy. Moreover, we show that the structure of the Kähler space provides a natural description of composite systems in real quantum mechanics.