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We investigate magento-oscillations in the specific heat of non-relativisticfermions with a Fermi surface minimally coupled to a fluctuating U(1) gaugefield. Our study is motivated by the recent observation of quantum oscillationsin the underdoped cuprates, and by theoretical models of pocket Fermi surfacesrealizing a non-Fermi liquid `algebraic charge liquid'. Our main result is thecomputation of the order 1/N correction to the Lifshitz-Kosevich expression forthe oscillation amplitude in the dirty limit in a model with N species offermions.

de Haas-van Alphen oscillations for non-relativistic fermions coupled to an emergent U(1) gauge field