非幺正相互作用、绝热条件、Haag定理和重整化
Nonunitary Interaction, Adiabatic Condition, Haag's Theorem and Renormalization
摘要：
哈格定理表明，在合理的量子场论中，相互作用场算符和自由场算符之间的变换不可能是幺正的。在这里，从物理学的角度重新审视了酉性的原始要求，以表明酉性不仅不是必需的，而且确实是不可能的。电动力学被用作一个例子。在经典的处理中，相互作用不能被自动地打开或关闭，因为能量守恒不能以物理上有意义的方式保持。在完全二次量子化理论中，即使系统处于真空状态，相互作用（或源）项也总是出现在运动方程中。因此，交互不能以物理方式或以其他方式打开或关闭。因此，从自由场到相互作用场的变换V（t）不能被解释为实际的时间演化。这使得V（t）的幺正性变得非常不必要，因为幺正性的最初原因是通过时间演化来保存概率（或能量）。指出由于V（t）的幺正化，散射矩阵中需要重整化的无穷项出现了。另一种方法来散射相互作用的领域的建议。
英文摘要：
Haag's theorem has shown that the transformation between interacting and free field operators in a reasonable quantum field theory cannot be unitary. Here, the original requirement of unitarity is revisited from a physical point of view to show not only that unitarity is not required but indeed not possible. Electrodynamics is used as an example. In a classical treatment the interaction cannot be turned on or off adiabatically as energy conservation cannot be maintained in a physically meaningful way. In a fully second quantized theory the interaction (or source) term is always present in the equation of motion even if the system is in the vacuum state. So, the interaction cannot be physically turned on or off adiabatically or otherwise. Hence, the transformation V(t) from free fields to interacting fields cannot be interpreted as an actual time evolution. This makes the unitarity of V(t)quite unnecessary as the original reason for unitarity was to conserve probability (or energy) through a time evolution. It is conjectured that the infinite terms in the scattering matrix that need renormalization appear due to the forcing of V(t)to be unitary. An alternate approach to scattering of interacting fields is suggested.
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