Formulation of spin-1 fields in deformed space-time with minimal length based on Quesne-Thachuk algebra

Abstract

Quesne-Thachuk algebra is a relativistic deformed algebra which leads to a nonzero minimal length. We present the formulation of the Duffin-Kemmer-Petiau field in 1 + 1 space-time based on Quesne-Thachuk algebra. It is shown that a modified field with two effective masses appears in theory. One heavy ghost mass which diverges as deformation of space-time vanishes and one regular mass that reduces to usual mass in this limit. To avoid dealing with particles of complex energy as well as complex mass, we found that the deformation parameter has to be below the threshold value: \( \beta=1/m^{2}\) , where m is the mass of field particle. This relation provided us with a bound for applicability of deformed Quesne-Thachuk algebra for the Duffin-Kemmer-Petiau theory. Based on our analysis by using the mass data of spin-1 mesons, the upper bound \( 10^{-7}\) - \( 10^{-9}\) MeV^-2 was found for the deformation parameter. On the other hand, this bound for the deformation parameter leads to a minimal length of order \( 10^{-16}\) - \( 10^{-17}\) m, which is compatible with recent experimental data. Also, we introduce a modified propagator for the generalized Duffin-Kemmer-Petiau field playing the role of usual propagator in ordinary quantum field theory.