Abstract
A quantum field theory (QFT) in its algebraic description typically admits many irregular states. We compare two criteria intended to select the physical states: the Hadamard condition, which works for free fields, and the modular nuclearity condition, which can be formulated in a general axiomatic setting. The latter is motivated by recent work in constructive QFT and by the older Hamiltonian nuclearity condition. We include a precise result at the one-particle level, obtained with G. Lechner, which suggests that all quasi-free Hadamard states are modularly nuclear, but the converse is false.
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