Abordagem relativística para o átomo de hidrogênio em um cenário de comprimento mínimo introduzido pela álgebra Lorentz-covariante de Quesne-Tkachuk

Abstract

One of the reasons for gravity can not be included in the standard model is its non-renormalizability. Almost all the proposals for the quantization of gravity leads to existence of a minimal length which acts as a natural regulator. That effect suggests a generalized uncertaintly relations between position and momentum operators what results in a modified commutation relation between these operators, and thus changing the whole structure of quantum mechanics. In this work we calculate the magnitude of this minimum length through the energy of the ground state of the hydrogen atom in Dirac’s theory, based on the Quesne-Tkachuck commutation relation. Comparing with experimental data, we obtained the value of the minimum length is orders of magnitude less than or equal to 10-20m