  We compare light-front quantization and instant-time quantization both at the
level of operators and at the level of their Feynman diagram matrix elements.
At the level of operators light-front quantization and instant-time
quantization lead to equal light-front time commutation (or anticommutation)
relations that appear to be quite different from equal instant-time commutation
(or anticommutation) relations. Despite this we show that at unequal times
instant-time and light-front commutation (or anticommutation) relations
actually can be transformed into each other, with it only being the restriction
to equal times that makes the commutation (or anticommutation) relations appear
to be so different. While our results are valid for both bosons and fermions,
for fermions there are subtleties associated with tip of the light cone
contributions that need to be taken care of. At the level of Feynman diagrams
we show for non-vacuum Feynman diagrams that the pole terms in four-dimensional
light-front Feynman diagrams reproduce the three-dimensional light-front
on-shell Hamiltonian Fock space formulation in which the light-front energy and
light-front momentum are on shell. However, because of circle at infinity
contributions we show that this equivalence fails for four-dimensional
light-front vacuum tadpole diagrams. Then, precisely because of these circle at
infinity contributions, light-front vacuum tadpole diagrams are not only
nonzero, they are actually equal to instant-time vacuum tadpole diagrams.
Light-front vacuum diagrams are not correctly describable by the on-shell
Hamiltonian formalism, and thus not by the closely related infinite momentum
frame prescription either. With the transformation from instant-time fields to
light-front fields being a spacetime translation, not only are instant-time
quantization and light-front quantization equivalent, they are unitarily
equivalent.
