A remark on the holonomy group of a normal state over a hyperfinite von Neumann algebra

摘要

We will show that in a hyperfinite von Neumann algebra M acting on a separable Hilbert space, there exists a constant N∈N such that for an arbitrary φ∈[0, 2] there are invertible a1,…,a_N ∈ M_+ with a_N...a_1=e~(iφ)II. As a consequence, it can be shown that U(1) is isomorphically contained in the holonomy group at every normal state over M.