Rigorous Hamiltonian and Lagrangian analysis of classical and quantum theories with minimal length

Understand

GUP is a phenomenological model aimed for a description of a minimal length in quantum and classical systems.

• However, the analysis of problems in classical physics is usually approached preferring a different formalism than the one used for quantum systems, and vice versa.
• Potentially, the two approaches can result in inconsistencies.
• Here, we eliminate such inconsistencies proposing particular meanings and relations between the variables used to describe physical systems, resulting in a precise form of the Legendre transformation.