# The Euclidean $\phi^4_2$ theory as a limit of an interacting Bose gas

@inproceedings{Frohlich2022TheE, title={The Euclidean \$\phi^4\_2\$ theory as a limit of an interacting Bose gas}, author={Jurg Frohlich and Antti Knowles and Benjamin Schlein and Vedran Sohinger}, year={2022} }

We prove that the complex Euclidean field theory with local quartic self-interaction in two dimensions arises as a limit of an interacting Bose gas at positive temperature, when the density of the gas becomes large and the range of the interaction becomes small. The field theory is supported on distributions of negative regularity, which requires a renormalization by divergent mass and energy counterterms. We obtain convergence of the relative partition function and uniform convergence of the…

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