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We show that the partition function of many classical models with continuousdegrees of freedom, e.g. abelian lattice gauge theories and statisticalmechanical models, can be written as the partition function of an (enlarged)four-dimensional lattice gauge theory (LGT) with gauge group U(1). This resultis very general that it includes models in different dimensions with differentsymmetries. In particular, we show that a U(1) LGT defined in a curvedspacetime can be mapped to a U(1) LGT with a flat background metric. The resultis achieved by expressing the U(1) LGT partition function as an inner productbetween two quantum states.

The U(1) Lattice Gauge Theory Universally Connects All Classical Models with Continuous Variables, Including Background Gravity