  Commutation or anticommutation relations quantized at equal instant time and
commutation or anticommutation relations quantized at equal light-front time
not only cannot be transformed into each other, they take completely different
forms. While they would thus appear to describe different theories, we show
that this is not in fact the case. By looking not at equal times but at unequal
times, we show that unequal instant-time commutation or anticommutation
relations are completely equivalent to unequal light-front time commutation or
anticommutation relations. Light-front quantization and instant-time
quantization are thus the same, with it being only the restriction to equal
times that makes them look different. However for fermions there is a caveat,
as the light-front anticommutation relations involve projection operators
acting on the fermion fields. Nonetheless, not only can one still derive
fermion unequal light-front time anticommutators starting from unequal
instant-time ones, one can even derive unequal instant-time fermion
anticommutators starting from unequal light-front time anticommutators even
though the fermion projection operators that are relevant in the light-front
case are not invertible. To establish the equivalence for gauge fields we
present a quantization procedure that does not involve zero-mode singularities
that are commonly encountered in light-front gauge field studies. We also study
time-ordered products of fields, and again show the equivalence despite the
fact that there are additional terms in the fermion light-front case. We
establish our results first for free theories, and then to all orders in
interacting theories though comparison of the instant-time and light-front
Lehmann representations. Finally, we compare instant-time Hamiltonians and
light-front Hamiltonians, and show that in the instant-time rest frame they
give identical results.
