Quantum reconstruction in terms of imaginary time

Abstract

Modern quantum simulations methods often use a fictitious imaginary time introduced by Feynman to exactly transform static quantum problems to dynamic imaginary time classical ones [1]. In addition to imaginary time simulation methods such as centroid molecular dynamics and path integral Monte Carlo, one can apply this quantum-classical isomorphism to self-consistent field theory (SCFT). An advantage of the field-theoretic perspective is that it can be exactly transformed into quantum density functional theory (DFT), meaning that the theorems of DFT (Hohenberg-Kohn and Mermin theorems) prove an equivalence between classical imaginary time SCFT dynamics and static quantum results [2]. Since imaginary time is assigned the same properties as regular time, one can replace the imaginary time in the SCFT equations with real time (a Wick rotation), which gives the equations of time-dependent DFT. The time-dependent DFT theorem (Runge-Gross theorem) then proves that one obtains all results of standard quantum mechanics from this imaginary time classical starting point. These results make it very tempting to consider treating imaginary time as an element of reality. This quantum reconstruction from imaginary time will be discussed, including a speculative look at treating imaginary time in the context of special relativity, with a preliminary comparison to the deformed special relativity of Magueijo and Smolin. [1] D. M. Ceperely, Reviews of Modern Physics 67, 279 (1995) [2] R. B. Thompson, Journal of Chemical Physics 150, 204109 (2019) [3] J. Magueijo and L. Smolin, Physical Review D 67, 044017 (2003)