Adaptation of quantum models to economic growth theories
Hugo Spring-Ragain
TL;DR
The paper tackles the limitation of classical deterministic growth models by introducing a quantum-inspired macroeconomic framework where core variables are non-commuting operators on a Hilbert space and the economy is described by a dynamic state. It develops a full formalism: a time-dependent Hamiltonian dictates evolution (via a Schrödinger-type equation), Dyson series and Magnus expansions manage noncommutativity, and a quantum production function arises from operator expectations. Uncertainty and fluctuations are modeled through operator commutation relations, Heisenberg-type inequalities, and Langevin dynamics, including time-dependent attenuation and nonlinear feedback. A Feynman path integral formulation is constructed to reinterpret the dynamics in a trajectory-based framework, enabling analysis of stability, attractors, and quantum corrections to classical Solow growth with potential applications to radical-uncertainty policy simulations.
Abstract
Traditional economic growth theories, grounded in deterministic and often linear frameworks, fail to adequately capture the inherent uncertainty, non-commutativity, and complex interdependencies of modern economies. This paper proposes a novel approach by transposing fundamental concepts of quantum mechanics-such as superposition, operator algebra, and path integrals-into the realm of macroeconomic modeling. Within this quantum framework, core economic variables (capital, labor, and technological progress) are redefined as non-commuting operators acting on Hilbert spaces, and the state of the economy is represented as a dynamic wave function governed by a time-dependent Hamiltonian. The evolution of this economic wave function follows a generalized Schr{ö}dinger equation, developed here through Dyson series and Magnus expansions. We also define a quantum production function as the expected value of a composite operator, capturing the probabilistic nature of economic output. By integrating uncertainty relations analogous to Heisenberg's principle, and modeling economic fluctuations via Langevin dynamics, we extend the model to include dissipation, feedback loops, and non-linear interactions between variables. Finally, a Feynman path integral formalism is constructed to provide an alternative trajectory-based interpretation of economic dynamics. This quantum-inspired framework offers a rigorous and flexible methodology to rethink macroeconomic modeling under radical uncertainty, with potential applications in dynamic policy simulations and innovation-driven growth.