A Criterion for the Free Character of Fields

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Abstract
It is shown that a field is a free field as soon as the states generated by the Heisenberg field and the incoming field operators operating on the vacuum coincide [statement (i)]. Several conclusions are drawn from statement (i) concerning the strong convergence of the field for t tending to infinity [statement (ii)], the uselessness of the local clothed particle representation [statement (iii)], and the diagonalization of the Hamiltonian [statement (iv)], as well as the time behavior of the mathematical vacuum [statement (v)].