  In this work, we present the technical details of the discussion presented in
[J.J. Relancio, L.Santamar\'ia-Sanz (2024) arXiv:2403.18772], where we
establish the basis of quantum theories of the free massive scalar, the massive
fermionic, and the electromagnetic fields, in a doubly special relativity
scenario. This construction is based on a geometrical interpretation of the
kinematics of these kind of theories. In order to describe the modified
actions, we find that a higher (indeed infinite) derivative field theory is
needed, from which the deformed kinematics can be read. From our construction
we are able to restrict the possible models of doubly special relativity to
particular bases that preserve linear Lorentz invariance. We quantize the
theories and also obtain a deformed version of the Maxwell equations. We
analyze the electromagnetic vector potential either for an electric point-like
source and a magnetic dipole. We observe that the electric and magnetic fields
do not diverge at the origin for some models described with an anti de Sitter
space but do for the de Sitter one in both problems.
