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We study Hamiltonian form of unfree gauge symmetry where the gauge parametershave to obey differential equations. We consider the general case such that theDirac-Bergmann algorithm does not necessarily terminate at secondaryconstraints, and tertiary and higher order constraints may arise. Given theinvolution relations for the first-class constraints of all generations, weprovide explicit formulas for unfree gauge transformations in the Hamiltonianform, including the differential equations constraining gauge parameters. Allthe field theories with unfree gauge symmetry share the common feature: theyadmit sort of "global constants of motion" such that do not depend on the localdegrees of freedom. The simplest example is the cosmological constant in theunimodular gravity. We consider these constants as modular parameters ratherthan conserved quantities. We provide a systematic way of identifying all themodular parameters. We demonstrate that the modular parameters contribute tothe Hamiltonian constraints, while they are not explicitly involved in theaction. The Hamiltonian analysis of the unfree gauge symmetry is precessed by abrief exposition for the Lagrangian analogue, including explicitly covariantformula for degrees of freedom number count. We also adjust the BFV-BRSTHamiltonian quantization method for the case of unfree gauge symmetry. The maindistinction is in the content of the non-minimal sector and gauge fixingprocedure. The general formalism is exemplified by traceless tensor fields ofirreducible spin $s$ with the gauge symmetry parameters obeying transversalityequations.

Hamiltonian constraints and unfree gauge symmetry