关于观测者同余的粒子产生的紫外渐近性
Ultraviolet asymptotics of particle creation with respect to a congruence of observers
摘要：
考虑了自由质量标量场关于观测者的一般同余的量子场论的构造，其正、负频率模式的分裂由瞬时哈密顿量的对角化定义.我们得到了真空中产生粒子的平均数的紫外渐近的显式表达式，证明了对于$D$维时空中观测者与$D\geqslant3$的一般同余，产生粒子的总数在正则化去除极限下在紫外域发散.这在闵可夫斯基时空中也是成立的。因此，在这种情况下，量子演化在正则化移除极限下不是幺正的。证明了在量子水平上，不是所有经典容许的观测者同余都是真的。也就是说，QFT关于一个观察者的同余的么正性是违反的，当这个同余的等时超曲面不是类空的，即使是一个有限截止的理论。这些结果的影响进行了讨论。
英文摘要：
The construction of quantum field theory (QFT) of a free massive scalar field with respect to a general congruence of observers is considered, the splitting into positive- and negative-frequency modes being defined by diagonalization of the instantaneous Hamiltonian. The explicit expression for the ultraviolet asymptotics of the average number of particles created from the vacuum is found. It is shown that, for a general congruence of observers in the $D$-dimensional spacetime with $D\geqslant3$, the total number of created particles diverges in the ultraviolet domain in the regularization removal limit. This holds even in the Minkowski spacetime. Therefore, in this case, the quantum evolution is not unitary in the regularization removal limit. It is proved that not all classically admissible congruences of observers are proper on a quantum level. Namely, unitarity of QFT with respect to a congruence of observers is violated when the equal time hypersurfaces of this congruence are not spacelike, even for a theory with a finite cutoff. The implications of these results are discussed.
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