In this work, we present two possible venues to accomodate the KF -type Lorentz-symmetry violating Electrodynamics in an N = 1-supersymmetric framework. A chiral and a vector superfield are chosen to describe the background that signals Lorentz-symmetry breaking. In each case, the K µνκλ -tensor is expressed in terms of the components of the background superfield that we choose to describe the breaking. We also present in detail the actions with all fermionic partners of the background that determine K µνκλ .

The properties of an extension of the New Massive 3D Gravity by scalar matter with Higgs-like self-interaction are investigated. Its peturbative unitarity consistency is verified for a family of cosmological Bounce solutions found by the superpotential method. They correspond to the lower bound λ = −1 of the BHT unitarity window and describe eternally accelerated 3D Universe between two initial/final stable dS 3 vacua states. 1

We will study the splitting in the energy spectrum of the hydrogen atom subjected to a uniform electric field (Stark effect) with the Heisenberg algebra deformed leading to the minimum length. We will use the perturbation theory for cases not degenerate (n = 1) and degenerate (n = 2), along with known results of corrections in these levels caused by the minimum length applied purely to the hydrogen atom, so that we may find and estimate the corrections of minimum length applied to the Stark effect.

We study the gauge sector of the Standard Model Extension (SME) with the Lorentz covariant deformed Heisenberg algebra associated to the minimum length. In order to find and estimate corrections, we clarify whether the violation of Lorentz symmetry and the existence of a minimum length are independent phenomena or are, in some way, related.With this goal, we analyze the dispersion relations of this theory.

We study the Einstein–Hilbert gravitation with the deformed Heisenberg algebra leading to the minimum length, with the intention to find and estimate the corrections in this theory, clarifying whether or not it is possible to obtain, by means of the minimum length, a theory, in D[Formula: see text]=[Formula: see text]4, which is causal, unitary and provides a massive graviton. Therefore, we will calculate and analyze the dispersion relationships of the considered theory.