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arXiv · 1912.09265

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

Vitaly Vanchurin
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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.

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Vitaly Vanchurin. 2019-12-19. Dual Path Integral: a non-perturbative approach to strong coupling. https://arxiv.org/abs/1912.09265

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