Dual Path Integral: a non-perturbative approach to strong coupling

TL;DR

This paper introduces a non-perturbative dual path integral method for calculating partition functions of strongly coupled quantum systems, potentially illuminating the emergence of space-time and gravity.

Contribution

It develops a novel iterative dual path integral approach to analyze strongly coupled quantum systems beyond perturbation theory.

Findings

Successfully applied to systems with various interaction orders

Provides a framework for understanding emergence of space-time and gravity

Offers a new non-perturbative computational tool

Abstract

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 three examples of strongly coupled systems with first-order, second-order and higher-order interactions and discuss a possible emergence of space-time, quantum field theories and general relativity in context of the dual path integral.