Structure of asymptotic fields associated with permanently confined degrees of freedom in quantum field theory

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Abstract
I give an interpretation of permanent color confinement which allows the existence of a single-particle state carrying any color representation, but forbids the existence of a scattering state with two or more separated particles each carrying a nonsinglet color representation. I show that the Haag in-field expansion of the Wightman field has a form consistent with this interpretation in all sectors of the second-quantized nonrelativistic harmonic oscillator. I replace the usual in-fields by the confined in-fields which, by construction, have nonvanishing matrix elements only between the vacuum and one-particle states. I propose that the occurrence of the confined in-field is the sine qua non of confinement in terms of asymptotic fields; and that the Haag expansion of the Wightman field in normal-ordered products of confined in-fields for fields carrying confined degrees of freedom, such as color, and ordinary in-fields for other fields, such as normal hadron fields, will be a useful tool to study confinement in relativistic theories, such as quantum chromodynamics.