Lie conformal algebra

Length scale

Economics

Momentum (technical analysis)

Quantum

Quantum gravity

Physics

Finance

Pure mathematics

Mathematics

Mathematical physics

Position (finance)

Theoretical physics

Quantum mechanics

Algebra over a field

Commutator

Scale (ratio)

Physics Letters B

In quantum gravity it is generally thought that a modified commutator of the form [xˆ,pˆ]=iħ(1+βp2) is sufficient to give rise to a minimum length scale. We test this assumption and find that different pairs of modified operators can lead to the same modified commutator and yet give different or even no minimal length. The conclusion is that the modification of the operators is the main factor in determining whether there is a minimal length. This fact - that it is the specific form of the modified operators which determine the existence or not of a minimal length scale - can be used to keep or reject specific modifications of the position and momentum operators in theory of quantum gravity.

Modified commutators are not sufficient to determine a quantum gravity minimal length scale