论文标题
幽灵问题从Pauli-Villars到四阶量子重力及其分辨率
Ghost Problems from Pauli-Villars to Fourth-Order Quantum Gravity and their Resolution
论文作者
论文摘要
我们回顾了从Pauli-Villars调节剂理论到当前流行的四阶衍生量子重力理论的量子场理论中幽灵问题的历史。尽管这些理论似乎都具有带负标准的统一性幽灵状态，但我们表明，实际上，这些幽灵状态仅出现，因为这些理论是在错误的希尔伯特空间中提出的。在这些理论中，哈密顿人不是冬宫，而是具有反向对称性的。因此，人们不能使用由州及其Hermitian共轭的内部产品。相反，必须使用与抗线性对称性相对于状态及其共轭的内部产品，而后一种内部产物是阳性的。这样，就可以在四个时空维度建立重力理论的量子理论。
We review the history of the ghost problem in quantum field theory from the Pauli-Villars regulator theory to currently popular fourth-order derivative quantum gravity theories. While these theories all appear to have unitarity-violating ghost states with negative norm, we show that in fact these ghost states only appear because the theories are being formulated in the wrong Hilbert space. In these theories the Hamiltonians are not Hermitian but instead possess an antilinear symmetry. Consequently, one cannot use inner products that are built out of states and their Hermitian conjugates. Rather, one must use inner products built out of states and their conjugates with respect to the antilinear symmetry, and these latter inner products are positive. In this way one can build quantum theories of gravity in four spacetime dimensions that are unitary.
