The SME gauge sector with minimum length

Abstract

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.

Fundamental length in classical electrodynamics

“…-Throughout this article, we have considered a series of arguments that could lead to the existence of a fundamental length in CED, a resolution limit in any experiment. Lorentz symmetry and "minimum length" seem to be related to each other since both are expected to be well grounded at low and high energies [11]. So, further research is needed in order to propose an experiment of the sort described, for example, in fig.…”

“…with a 0 > 0, and (11) we find only two firstorder differential equations: It is straightforward to show that these equations are equivalent (as they must). So, we can use either one of them for our calculations.…”

“…Many efforts have been made to build classical and quantum theories (a) E-mail: stanleybruces@gmail.com (b) E-mail: jdiaz@udec.cl founded on this view, such as the ones given in refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The essential conjecture in some of these theories is that on a quite short time δt the system does not evolve steadily under unitary evolution but somewhat in a succession of similar transformations.…”

The short-distance behavior of an Abelian Proca model based on a one-parameter extension of the covariant Heisenberg algebra

“…In recent years, reformulation of Maxwell electrodynamics in the presence of a minimal length scale and the study of short-distance behavior of Maxwell theory has attracted a considerable attention among researchers in quantum field theory [7][8][9][10]. In Ref.…”