A physically meaningful local concept of temperature is introduced in quantum field theory on curved spacetime and applied to the example of a massless field on de Sitter space. It turns out in this model that the equilibrium (Gibbs) states which can be prepared by a geodesic observer have in general a varying temperature distribution in the neighborhood of the geodesic and may not even allow for a consistent thermal interpretation close to the horizon. This result, which can be traced back to the Unruh effect, illustrates the failure of a global notion of temperature in curved spacetime and reveals the need for a local concept, as presented here.
Abstract. In this paper we investigate the energy distribution of states of a linear scalar quantum field with arbitrary curvature coupling on a curved spacetime which fulfill some local thermality condition. We find that this condition implies a quantum energy inequality for these states, where the (lower) energy bounds depend only on the local temperature distribution and are local and covariant (the dependence of the bounds other than on temperature is on parameters defining the quantum field model, and on local quantities constructed from the spacetime metric). Moreover, we also establish the averaged null energy condition (ANEC) for such locally thermal states, under growth conditions on their local temperature and under conditions on the free parameters entering the definition of the renormalized stress-energy tensor. These results hold for a range of curvature couplings including the cases of conformally coupled and minimally coupled scalar field.
Abstract. Two recent deformation schemes for quantum field theories on two-dimensional Minkowski space, making use of deformed field operators and Longo-Witten endomorphisms, respectively, are shown to be equivalent. Mathematics Subject Classification (2010). 81T05, 81T40.Keywords. deformations of quantum field theories, two-dimensional models, modular theory. Deformations of QFTs by Inner Functions and Their RootsIn recent years, there has been a lot of interest in deformations of quantum field theories [1,3,[8][9][10]12,[17][18][19][20][21][22]24] in the sense of specific procedures modifying quantum field theoretic models on Minkowski space, mostly motivated by the desire to construct new models in a non-perturbative manner. Various constructions have been invented, relying on different methods such as smooth group actions, noncommutative geometry, chiral conformal field theory, boundary quantum field theory, and inverse scattering theory.In many situations, it is possible to set up the deformation in such a way that Poincaré covariance is completely preserved and locality partly. More precisely, often the deformation introduces operators which are no longer localized in arbitrarily small regions of spacetime, but rather in unbounded regions like a Rindler wedge W := {x ∈ R d : x 1 > |x 0 |}. In the operator-algebraic framework of quantum field theory [14], such a wedge-local Poincaré covariant model can be conveniently described by a so-called Borchers triple (M, U, ) [4,8], consisting of a GL and JS supported by FWF project P22929-N16 "Deformations of quantum field theories". Y. Tanimoto supported by Deutscher Akademischer Austauschdienst.
We review different definitions of the current density for quantized fermions in the presence of an external electromagnetic field. Several deficiencies in the popular prescription due to Schwinger and the mode sum formula for static external potentials are pointed out. We argue that Dirac's method, which is the analog of the Hadamard pointsplitting employed in quantum field theory in curved space-times, is conceptually the most satisfactory. As a concrete example, we discuss vacuum polarization and the stress-energy tensor for massless fermions in 1+1 dimension. Also a general formula for the vacuum polarization in static external potentials in 3+1 dimensions is derived.
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