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.

中文翻译：

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比较光前量化与即时量化

我们在算子级别和费曼图矩阵元素级别比较了光前量化和即时量化。在算子层面，光前量化和即时量化导致等光前时间换向（或反换向）关系似乎与等即时时间换向（或反换向）关系完全不同。尽管如此，我们表明，在不相等的时刻，瞬时和光前对易（或反对换）关系实际上可以相互转化，只是对相等时间的限制使对易（或反对换）关系看起来是太不同了。虽然我们的结果对玻色子和费米子都有效，对于费米子，需要注意与光锥尖端贡献相关的微妙之处。在费曼图的水平上，我们为非真空费曼图展示了四维光前费曼图中的极项再现了三维光前壳上哈密顿福克空间公式，其中光前能量和光锋势头在壳上。然而，由于无穷远贡献的圆，我们表明这种等价性对于四维光前真空蝌蚪图无效。那么，正是由于这些无穷大的圆贡献，光前真空蝌蚪图不仅非零，它们实际上等于瞬时真空蝌蚪图。壳上哈密顿形式主义不能正确描述光前真空图，因此也不是由密切相关的无限动量框架处方决定的。由于从瞬时场到光前场的变换是一种时空平移，所以瞬时量化和光前量化不仅是等价的，而且是酉等价的。