  Differences between vector potentials in different gauges contain no dynamics
in both classical and quantum electrodynamics and chromodynamics. Consequently,
once gauge invariance is established, results calculated in non-covariant
gauges can be expected to agree with results obtained in covariant gauges in
all Lorentz frames. We show in particular that canonical quantization in the
Coulomb gauge can be used without giving up explicit gauge invariance.
Quantization in the Coulomb gauge is particularly simple because it involves
only the two transverse photons/gluons present in all gauges. These transverse
photons/gluons reside on a 2-dimensional physical plane in momentum space
perpendicular to the photon/gluon momentum {\bf k}. Explicit expressions are
given for the basic momentum, spin and orbital angular momentum field operators
of photons/gluons in the Coulomb gauge. Their properties are discussed in some
detail. In particular, these field operators are shown to be more complicated
than the corresponding operators in quantum mechanics which they also contain.
