Abstract
We consider the global structure of momentum space Π3, 1 in a field theory which is covariant with respect to the action of global conformal group G. We show that Π3, 1 is a homogeneous space for G which coincides with (S3×S1)/Z2 compact space. The radius of momentum space determines the natural invariant ultraviolet cutoff which may take the form of a Pauli-Vilars form factor in perturbation theory. We demonstrate in the case of the massless λφ4 theory how the conventional ultraviolet divergences which appear in the flat momentum space are regularized in Π3, 1 global momentum space.
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Budinich, P., Raczka, R. Global properties of conformally flat momentum space and their implications. Found Phys 23, 599–615 (1993). https://doi.org/10.1007/BF01883768
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DOI: https://doi.org/10.1007/BF01883768