Foundations of Quantum Mechanics: Principles, Axiomatizations, Formalisms, Interpretations

Special Issue Information Dear Colleagues, We call for contributions to a Special Issue of the MDPI Journal Applied Sciences. This issue will provide a repository of original research and survey works dealing with possible paradigms of the foundations, axiomatizations, mathematical formalisms and interpretations of quantum mechanics. The foundations of quantum mechanics appear to have been recently revitalized for several reasons, including: (i) the growing importance of quantum computation and quantum information theory; (ii) studies of the relationships between quantum theory and relativity; (iii) the search for a more realistic interpretation; (iv) proposals to reconstruct quantum theory from new basic axioms in a coherent and more realistic fashion. In the last years, we have also seen numerous insights in the understanding and classification of non-locality and contextuality, using tools from sheaf theory and cohomology, as well as operator algebras (also based upon Schwartz distribution spaces) and category theory. We are also interested in papers on quantum statistical mechanics addressing fundamental issues. The modern QM foundations are inextricably interlaced and merged with mathematical structures and their theories: category theory; convex analysis; operator algebras; measure theory; Schwartz distribution spaces; nuclear spaces; and general functional analysis. Indeed, the foundations and axiomatizations of quantum mechanics need various mathematical formalisms to model physical systems and provide meaningful predictions. Regrettably, sometimes the physical interpretations that emerge are rather ambiguous, especially concerning the implications of mathematical formalisms on the underlying physical nature and its evolution. Starting from the classic critical observations of Einstein, Schroedinger, Bell, Dirac, Heisenberg, and so on, we desire to emphasize the following themes: •fundamental models of quantum mechanics and their interpretations; •entanglement and its consequences; •realism; •non-locality; •delayed choice experiments; •quantum eraser experiments; •interferometer experiments; •Bell-type theorems. We also encourage works in emergent quantum mechanics and other research programs interested in a realist interpretations of quantum mechanics. We recall, in this respect, the research of David Bohm. We welcome, in this context, papers trying to build up a non-local pilot-wave framework compatible with Einstein's relativity. Our ultimate aim could be summarized as facing the basic problems of the rigorous, coherent foundation and interpretation of quantum mechanics. Other potential topics include, but are not limited to: •Interpretations of different quantum mechanics paradigms; •Mathematical formalisms and axiomatization of quantum mechanics; •Non-locality and violation of Bell inequalities; •Quantum probabilities and contextuality; •Quantum causality and ontology; •Information measures in quantum theory; •Self-organization and quantum emergence; •Non-local hidden variable theories; •Quantum relativity and emergent space–time; •Bohm–De Broglie relativistic theory. Prof. Dr. David Carfì Prof. Dr. Alexei Kushner Prof. Dr. Vladimir Balan Prof. Dr. Samvel Haroutunian Eng. Dr. Alessia Donato Guest Editors