My research interests span a range of topics from quantization of gauge theories such as general relativity and Yang-Mills theory to philosophical foundations of both gauge theories and quantum mechanics. With respect to the philosophy of gauge theories, I analyzed the physical content of the heuristic “gauge argument” in Yang-Mills theory and the ontological assumptions entailed by the passage from a global to a local symmetry, I distinguished the two independent first principles of Yang-Mills theory—namely internal relativity and internal background independence—, and I proposed a conceptual interpretation of the BRST formalism. With respect to the philosophy of quantum mechanics, I’m working on a formalism which had never been addressed—up to my knowledge—by philosophers of quantum mechanics, namely geometric quantization. I showed that the corresponding technical shift in the presentation of quantum mechanics is the formal counterpart of a radically different conceptual comprehension of quantum physics. Indeed, this new avenue for research in the philosophy of quantum mechanics has already led to unexpected results. In particular, I showed that quantum mechanics endorses a realistic quantum ontology of physical systems. This conclusion contests the widespread idea according to which the passage from classical mechanics to quantum mechanics comes hand in hand with a weakening of the notion of physical objectivity. According to the proposed quantum ontology, quantum mechanics provides—unlike classical mechanics—a complete description of all the objective properties of physical systems.
Gabriel Catren, Nature Absolue – Speculative Philosophy of the Physico-Mathematical
Philosophy of Mechanics: Mathematical Foundations Workshop Feb 12-14, 2014 (website poster)
“Translation: the philosopher’s task”, interview with Gabriel Catren