Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Abstract Several models of quantum gravity predict the emergence a minimal length at Planck scale. This is commonly taken into consideration by modifying Heisenberg uncertainty principle generalized principle. In this work, we study implications polynomial on harmonic oscillator. We revisit both analytic and algebraic methods, deriving exact form algebra in terms new position momentum operators. show that energy spectrum eigenfunctions are affected non-trivial way. Furthermore, set ladder operators derived which factorize Hamiltonian exactly. The above formalism finally exploited to construct field theoretic toy model based