In this letter the algebraic renormalization method, which is independent of any kind of regularization scheme, is presented for the parity-preserving QED 3 coupled to scalar matter in the symmetric regime, where the scalar assumes vanishing vacuum expectation value, ϕ =0. The model shows to be stable under radiative corrections and anomaly free.The study of gauge field theories in 3 space-time dimensions [1] has been well-supported by a possible field-theoretical approach to describe some Condensed Matter phenomena, such as High-T c Superconductivity and Quantum Hall Effect [2,3]. Some Abelian models have been proposed in this direction, namely, the QED 3 and τ 3 QED 3 [4,5].One of the interesting properties of 3-dimensional gauge field theories is the Landau gauge finiteness of non-Abelian Chern-Simons theories [6].The confinement of massive electrons in 3 space-time dimensions is a remarkable characteristic of this lower dimensional space [7]. Recently, it was shown by using the Bethe-Salpeter equations that in a parity-preserving QED 3 there are bound states in electron-positron systems, positronium states [8].In a recent work [9], a parity-preserving QED 3 with spontaneous breaking of a local U(1)-symmetry was proposed. The breakingdown is accomplished by a sixth-power potential. It was shown that electrons scattered in D=1+2 can experience a mutual attractive interaction, depending on their spin states, where the intermediate bosons involved in *

Considering (2, 0)-supersymmetric non-linear σ-models defined over Kählerian coset manifolds, we discuss the gauging of the isotropy and isometry groups in (2, 0)-superspace and present the action coupling these σ-models to the (2, 0)-Yang-Mills supermultiplets.

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I S S N 2 3 4 7 -3 4 8 7 V o l u m e 1 3 N u m b e r 3 J o u r n a l o f A d v a n c e s i n P h y s i c s 4751 | P a g e M a r c h 2 0 1 7 w w w . helayel@cbpf.br ABSTRACTIn this contribution, we build up an axiomatic local metric derivative that exhibits Mittag-Leffler function as an eigenfunction and is valid for low-level fractionality, whenever the order parameter is close to 1. This version of deformed (or metric) derivative may be a possible alternative to the versions worked out by Jumarie and the so-called local fractional derivative also based on Jumarie's approach. With rules similar to the classical ones, but with a systematic axiomatic basis in the limit pointed out here, we present our results and some comments on the limits of validity for the controversial formalism found in the literature of the area. Indexing terms/KeywordsDeformed Derivatives, Metric Derivatives, Fractal Continuum, Mittag-Leffler Function, Eigenfunction, Low Level Fractionality . Academic Discipline And Sub-DisciplinesPhysics/Mathematics. SUBJECT CLASSIFICATIONMathematical Methos in Physics. TYPE (METHOD/APPROACH)Theoretical: Mathematical Methos in Physics-Deformed or metric derivatives.

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