标题： 费米子和希格斯量子场论的运动学希尔伯特空间 显示英文标题

标题： Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field Theories

摘要： 我们扩展了最近为紧致规范群的连接微分同胚不变理论开发的运动学框架，以适用于包含连接、费米子和希格斯场的微分同胚不变量子场论的情况。 该框架适合将物质与量子引力耦合。 微分同胚不变性的存在迫使我们选择一种相当非福克类型的表示：连接的基本激发沿着开弦或闭弦，而费米子或希格斯场的基本激发则位于弦的端点。 尽管如此，我们仍能够将经典的实性条件提升为量子伴随关系，这反过来唯一地确定了支撑希尔伯特空间的规范和微分同胚不变的概率测度。 这项工作中大部分的费米子部分独立于Baez和Krasnov的最近预印本以及Rovelli和Morales-Tecótl的早期工作，因为我们使用了新的规范费米子变量，即所谓的格拉斯曼值半密度，这使我们能够解决困难的费米子伴随关系。 显示英文摘要

摘要： We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also fermions and Higgs fields. This framework is appropriate for coupling matter to quantum gravity. The presence of diffeomorphism invariance forces us to choose a representation which is a rather non-Fock-like one : the elementary excitations of the connection are along open or closed strings while those of the fermions or Higgs fields are at the end points of the string. Nevertheless we are able to promote the classical reality conditions to quantum adjointness relations which in turn uniquely fixes the gauge and diffeomorphism invariant probability measure that underlies the Hilbert space. Most of the fermionic part of this work is independent of the recent preprint by Baez and Krasnov and earlier work by Rovelli and Morales-Tec\'otl because we use new canonical fermionic variables, so-called Grassman-valued half-densities, which enable us to to solve the difficult fermionic adjointness relations.