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Description
The gauge symmetry is said unfree if the gauge transformation leaves the action functional invariant, provided that the gauge parameters are constrained by a system of partial differential equations. The most known example of this phenomenon is the volume-preserving diffeomorphism, being the gauge symmetry of unimodular gravity. Given the distinctions of the unfree gauge symmetry from the symmetry with unrestricted gauge parameters, the algebra of gauge transformations is essentially different. This affects all the key constituents of general gauge theory, including the second Noether theorem, Hamiltonian constrained formalism, BRST complex, etc. We summarize the modifications of general gauge theory worked out to cover the case of unfree gauge symmetry. The general formalism is exemplified by the higher spin models with unfree gauge symmetry.
