  We reformulate gauge theories in analogy with the vierbein formalism of
general relativity. More specifically, we reformulate gauge theories such that
their gauge dynamical degrees of freedom are local fields that transform
linearly under the dual representation of the charged matter field. These local
fields, which naively have the interpretation of non-local operators similar to
Wilson lines, satisfy constraint equations. A set of basis tensor fields are
used to solve these constraint equations, and their field theory is
constructed. A new local symmetry in terms of the basis tensor fields is used
to make this field theory local and maintain a Hamiltonian that is bounded from
below. The field theory of the basis tensor fields is what we call the basis
tensor gauge theory.
