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One of the most well known relativistic field theory models is the Thirringmodel (TM). Its realization can demonstrate the famous prediction for therenormalization of mass due to interactions. However, experimental verificationof the latter requires complex accelerator experiments whereas analyticalsolutions of the model can be extremely cumbersome to obtain. In this work,following Feynman's original proposal, we propose a alternative quantum systemas a simulator of the TM dynamics. Here the relativistic particles aremimicked, counter-intuitively, by polarized photons in a quantum nonlinearmedium. We show that the entire set of regimes of the Thirring model -- bosonicor fermionic, and massless or massive -- can be faithfully reproduced usingcoherent light trapping techniques. The sought after correlations' scalings canbe extracted by simple probing of the coherence functions of the light usingstandard optical techniques.

Mimicking interacting relativistic theories with stationary pulses of light