  We show that the partition function of many classical models with continuous
degrees of freedom, e.g. abelian lattice gauge theories and statistical
mechanical models, can be written as the partition function of an (enlarged)
four-dimensional lattice gauge theory (LGT) with gauge group U(1). This result
is very general that it includes models in different dimensions with different
symmetries. In particular, we show that a U(1) LGT defined in a curved
spacetime can be mapped to a U(1) LGT with a flat background metric. The result
is achieved by expressing the U(1) LGT partition function as an inner product
between two quantum states.
