论文标题
时空事件的量子测量
Quantum Measurement of Space-Time Events
论文作者
论文摘要
相对论系统的相空间可以用综合的Minkowski空间的未来管识别。除了复杂的结构和符号结构外，未来的管被视为八维实际歧管，还具有天然的阳性降低的riemannian指标，该指标可容纳不确定的Minkowski空间度量的基本几何形状以及其对称组。然后可以构建15个参数组合群转换的统一表示，该转换作用于未来管的正方形综合性霍尔伯特空间上。这些结构足以允许人们提出相位空间事件的量子理论。特别是，量子测量理论可以在相对论的环境中，基于使用正算子的使用值衡量标准，用于检测相空间事件，从而使一个人可以将概率分配给在显着的共互联框架中为关节时空和四摩梅特测量结果分配的概率。这导致了相对论量子理论中的相位事件的定位定理，该理论由相关的康普顿波长决定。
The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the future tube, seen as an eight-dimensional real manifold, is endowed with a natural positive-definite Riemannian metric that accommodates the underlying geometry of the indefinite Minkowski space metric, together with its symmetry group. A unitary representation of the 15-parameter group of conformal transformations can then be constructed that acts upon the Hilbert space of square-integrable holomorphic functions on the future tube. These structures are enough to allow one to put forward a quantum theory of phase-space events. In particular, a theory of quantum measurement can be formulated in a relativistic setting, based on the use of positive operator valued measures, for the detection of phase-space events, hence allowing one to assign probabilities to the outcomes of joint space-time and four-momentum measurements in a manifestly covariant framework. This leads to a localization theorem for phase-space events in relativistic quantum theory, determined by the associated Compton wavelength.
