标题： 量子阿贝尔对偶的Hadamard态 显示英文标题

标题： Hadamard states for quantum Abelian duality

摘要： 阿贝尔对偶性通过结合微分上同调和局部协变量子场论自然实现。 这导致了一个C$^*$-代数的可观测量，它涵盖了磁通量和电通量的同时离散化。 我们讨论为这种代数分配物理上行为良好的状态以及相关GNS三元组的性质。 我们证明可观测量的代数可以分解为三个C$^*$-代数的适当张量积：第一个因子编码动力学信息，而另外两个捕捉对应于电通量和磁通量的拓扑数据。 在前一个因子上，我们展示了一个两点关联函数具有与哈达玛态相同奇异结构的状态。 在拓扑因子上也指定合适的对应物，我们得到了整个理论的状态，最终提供了阿贝尔对偶性的单位实现。 显示英文摘要

摘要： Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a C$^*$-algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states to such algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three C$^*$-algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors we obtain a state for the full theory, providing ultimately a unitary implementation of Abelian duality.