λ?~4 KINK AND SINE-GORDON SOLITON IN THE GUP FRAMEWORK

摘要

We consider λ?~4 kink and sine-Gordon soliton in the presence of a minimal length uncertainty proportional to the Planck length. The modified Hamiltonian contains an extra term proportional to p~4 and the generalized Schr?dinger equation is expressed as a fourth-order differential equation in quasiposition space. We obtain the modified energy spectrum for the discrete states and compare our results with one-loop resummed and Hartree approximations for the quantum fluctuations. We finally find some lower bounds for the deformations parameter, so that the effects of the minimal length have the dominant role.