Exploring the Relevance of Thermal Spacetime Quantum Mechanics to Data Science and Medical Imaging

Medical imaging can produce time series of three dimensional data, for example, in fMRI. The spacekime (spacetime plus an imaginary time) approach of Dinov et al. promotes the time dimension into a complex quantity in order to help analyze data. Standard quantum techniques such as path integral Monte Carlo and centroid molecular dynamics similarly analyze quantum mechanical phenomena using imaginary time, where the imaginary time plays the role of a thermal parameter. A closely related quantum approach, which also uses a thermal spacetime, is polymer self-consistent field theory (SCFT). SCFT can be shown to be equivalent to quantum density functional theory (DFT), in which a one-particle density contains all the information of a quantum system instead of a many-particle configuration-space wave function. For this reason, DFT is used throughout science and engineering as a practical way to perform complicated quantum computations. Since spacekime data science using imaginary time is relevant to medical imaging, some very basic mappings between spacekime and thermal spacetime quantum mechanics using SCFT will be discussed to explore the possibility of any similar relevance.