Abstract
The authors develop a nonperturbative approach to the quantization of finite-dimensional gauge systems in the framework of the GuptaBleuler formalism. A finite-dimensional gauge theory is considered with Abelian symmetry group (scalar electrodynamics on a finite lattice). Some problems of the constructive construction of a state space with indefinite metric are discussed. The construction of the auxiliary definite metric, and the distinguishing of the physical sector, are examined.
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