Effect of RGUP on the nonlinear Klein-Gordon model with spontaneous symmetry breaking

Abstract

In the framework of the relativistic generalized uncertainty principle (RGUP), we study the nonlinear Klein-Gordon field with ${\varphi }^4$ self-interaction. This generalization comes from the quantum gravity theories that predict the existence of a minimal measurable length scale. The quantum gravity effects slightly modify the momentum and change the Lagrangian density of the field. This model, specifically in the context of spontaneous symmetry breaking, is so fruitful and leads us to many interesting phenomena. Due to the complexity of the consequent equations, the model is normally studied via perturbation mechanisms. However, here, we apply a generalized $tanh$-method which supposed that the field solutions should be $sech$-functions of segments of space and time. By this extended method, we find some more general solutions with respect to our previous work \cite{Mir1}. Several solutions can be found but we select only the normalizable and bounded solitary fields. The energy spectrum of each field solution is obtained in an analytical form and discussed. The modification parameter of the corresponding RGUP is estimated by using the rest energy of the mass of the Higgs boson.

arXiv comment16 pages, 6 figures

References in corpus (15)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum gravity and minimum length
• Universality of Quantum Gravity Corrections
• Nonpointlike Particles in Harmonic Oscillators
• Phenomenological Implications of the Generalized Uncertainty Principle
• Measurement of quantum states of neutrons in the Earth's gravitational field
• Maximal Localisation in the Presence of Minimal Uncertainties in Positions and Momenta
• Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator
• Lorentz-covariant deformed algebra with minimal length
• Generalized uncertainty principles and quantum field theory
• Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length
• Quantum field theory with the generalized uncertainty principle I: scalar electrodynamics
• The solitary solutions of nonlinear Klein-Gordon field with minimal length
• Solitons in the Einstein universe
• Steady flows, nonlinear gravitostatic waves and Zeldovich pancakes in a Newtonian gas