Abstract
The possibility of constructing gauge invariant charge densities in classical gauge theory is investigated. For the Yang-Mills-Dirac fields in the Minkowski space, it is shown that, unless the colour label belongs to the centre of the colour algebra, gauge invariant charge densities depend non-locally on the field variables and have non-local Poisson brackets. A quantization leading to observable charge density operators with commutators related to the classical Poisson bracket would violate the locality axiom of quantum field theory. For the Yang-Mills-Dirac fields in a bag the colour algebra is trivial and the colour charges vanish identically. In this sense the Yang-Mills-Dirac theory has to be considered as confining on the basis of a purely mathematical reasoning.
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