Regular Article – Theoretical Physics
Dual path integral: a non-perturbative approach to strong coupling
Department of Physics, University of Minnesota, 55812, Duluth, MN, USA
2 Duluth Institute for Advanced Study, 55804, Duluth, MN, USA
Accepted: 3 March 2021
Published online: 17 March 2021
We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path integral of a dual system. The dual path integral is derived starting from non-interacting subsystems at zeroth order and then by introducing couplings of increasing complexity at each order of an iterative procedure. These orders of interactions play the role of a dual time and the full quantum partition function is expressed as a transition amplitude in the dual system. More precisely, it is expressed as a path integral from a deformation-operators dependent initial state at zero time/order to the inverse-temperature dependent final state at later time/order. We provide examples of strongly coupled systems with up to first-order interactions (e.g. Ising model) and arbitrary high-order interactions (e.g. QFT). We also discuss a possible emergence of space-time, quantum field theories and general relativity in context of the dual path integral.
© The Author(s) 2021
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