Quantum Gauge Theory
See
gauge theory
for the classical preliminaries. In order to
quantize
a gauge theory, like for example
Yang-Mills
theory,
Chern-Simons
or
BF model
, one method is to perform a
gauge fixing
. This is done in the
BRST
and
Batalin-Vilkovisky
formulation. Another is to factor out the symmetry by dispensing with
vector potentials
altogether (they're not physically
observable
anyway) and work directly with
Wilson loops
,
Wilson lines
contracted with other charged fields at its endpoints and
spin networks
. Older approaches to quantization for
Abelian
models use the
Gupta-Bleuler
formalism with a "
semi-Hilbert space
" with an
indefinite
sesquilinear form
. However, it is much more elegant to just work with the
quotient space
of vector field configurations by gauge transformations. An alternative approach using lattice approximations is covered in (
Wick rotated
)
lattice gauge theory
.
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