Extending Segal’s postulates of quantum mechanics to the complex case Velasco Collado, María Victoria Aycart-Maldonado, Enrique Mathematical physics Complex systems Quantum theory Funding for open access publishing: Universidad de Granada/CBUA. This study was funded by Vicerrectorado de Investigación y Transferencia, Universidad de Granada and Instituto de Matemáticas, Universidad de Granada (Maria de Maeztu). In this paper, we review Segal’s postulates for general Quantum Mechanics, updating and clarifying their mathematical formulation to simplify them. Our approach provides additional insights as well as a pathway to easily contribute new results to the body of knowledge on systems of observables. Moreover, we introduce the notion of complex system of observables, which arises naturally from the analysis carried out. As we show, these last systems of observables are related to the classical (real) ones through the process of complexification. Taking advantage of this, algebraic systems of observables are completely determined in both the real and complex cases. 2025-12-11T12:15:12Z 2025-12-11T12:15:12Z 2025-06-13 journal article Velasco, M.V., Aycart-Maldonado, E. Extending Segal’s postulates of quantum mechanics to the complex case. Arab. J. Math. 14, 567–587 (2025). https://doi.org/10.1007/s40065-025-00530-2 2193-5343 2193-5351 https://hdl.handle.net/10481/108730 10.1007/s40065-025-00530-2 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Springer Nature