We consider field-theoretic models, one consisting purely of scalars, the other also involving fermions, that couple to a set of constant background coupling coefficients transforming as a symmetric observer Lorentz two-tensor. We show that the exact propagators can be cast in the form of a Kallen-Lehmann representation. We work out the resulting form of the Feynman propagators and the equal-time field commutators, and derive sum rules for the spectral density functions.
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