Remarks on generalized uncertainty principle induced from constraint system

TL;DR

This paper derives generalized uncertainty principle commutation relations from a constrained Hamiltonian system using Dirac brackets, offering a new perspective without assuming minimal length.

Contribution

It introduces a method to obtain generalized uncertainty relations from constrained Hamiltonian systems, avoiding the usual minimal length assumption.

Findings

Dirac brackets reproduce extended commutation relations

Method connects constrained systems with generalized uncertainty principles

Provides a new derivation approach for GUP relations

Abstract

The extended commutation relations for a generalized uncertainty principle have been based on the assumption of the minimal length in position. Instead of this assumption, we start with a constrained Hamiltonian system described by the conventional Poisson algebra and then impose appropriate second class constraints to this system. Consequently, we can show that the consistent Dirac brackets for this system are nothing but the extended commutation relations describing the generalized uncertainty principle.