On grand canonical Green functions in the Rindler wedge

We prove that certain scalar massless charged Green functions, found by Guimarães and Linet in the manifold around a straight cosmic string carrying a magnetic flux, can be analytically continued in the Rindler space together with the corresponding renormalized stress tensor. These functions seem to be related to grand-canonical ensemble states of a massless scalar charged field in the Rindler wedge. In fact, they satisfy customary requirements of the thermal quantum field theory for every value of the chemical potential μ. Nevertheless, on a physical ground, one expects that these two-point functions should not define quantum states a priori, because relativistic massless particles require μ = 0 necessarily. This follows directly from the definition of partition function in a finite spatial volume. Actually, the considered situation is more complicated because the spatial section of the Rindler wedge has an infinite volume and no partition function can be directly defined. The solution of this somehow weird problem arises from algebraic approaches. These functions does not define a positive-defined sesquilinear functional on the algebra of 3-smeared observables, thus no GNS construction procedure can be implemented and no Hilbert-Fock representation can be built up. Some remarks are finally reported on the massive case, where our negative result should not arise and the analytic continuation of the Guimarães-Linet Green functions should define true grand canonical Rindler quantum states. PACS number(s): 03.70.+k, 04.62.+v, 11.10.Cd, 11.10.Wx e-mail: [email protected]