  The work aims effective and low-dimensional systems. Some different contexts
involving gravitational and electromagnetic interactions are investigated. The
electromagnetic one approaches bosonic and fermionic Effective Quantum Field
Theories non-minimally coupled in three spacetime dimensions submitted to the
expansion of Foldy-Wouthuysen Transformation, what generates (non-)relativistic
corrections. A study of the effects of an external electromagnetic field
derived from the Maxwell-Chern-Simons Electrodynamics on the obtained
interactions are executed, as well as the impact produced by the dimensional
reduction on expanded higher dimensional fermionic system in comparison to the
low-dimensional one. In the scenario of gravitational effective model, scalar
and fermionic particle scatterings reveal inter-particles interactions beyond
monopole-monopole, leading to velocity and spin contributions, and the results
are compared to a modified Electrodynamics effective model. A non-perturbative
model resourcing to Casual Dynamics Triangulation data is adopted to serve as
consistency check of the potentials resultants. Low-dimensional Maxwell-Higgs
effective models with modified kinetic terms are studied, submitting them to a
Bogomol'nyi prescription-type for calculation of inferior (non-trivial) bound
energy and the self-dual equations. Vortex solutions for gauge field
non-specified by an ansatz are achieved and their topological feature detailed.
