The Nambu–Goldstone boson model with the maximal momentum hypothesis

The Nambu–Goldstone boson model is examined within the covariant extension of the generalized uncertainty principle. This formalism introduces a Lorentz-invariant minimal length or, alternatively, a maximal momentum into the theory, depending on the sign of the deformation parameter β 0 . The Nambu–Goldstone boson model plays a fundamental role in quantum field theory and serves as a prototype for describing diverse physical phenomena across different areas of physics. As a consequence of the spontaneous breaking of the U ( 1 ) symmetry, the model gives rise to one massless and one massive scalar particle. Exact analytical solutions are obtained using the sech -method, enabling the identification of solitonic configurations for each scalar field. The two-field system is subsequently normalized, and its total energy is calculated. The exact solutions of the model correspond to the case β 0 < 0 , indicating the existence of a maximal momentum within the framework. Moreover, for these solutions, β 0 is found to be inversely proportional to the square of the mass of the massive scalar field. Consequently, this relation defines an upper bound interval for the parameter | β 0 | .