Sub-bosonic (deformed) ladder operators

TL;DR

This paper introduces a class of deformed ladder operators with fuzzy energy addition/subtraction, leading to modified algebraic relations and potential observable deviations in quantum field theories.

Contribution

It presents a novel formalism of sub-bosonic operators derived from a rigorous notion of fuzziness, altering standard commutation relations and eigenenergies.

Findings

Deformed operators induce modified eigenenergies.

Altered commutation relations with a simple algebraic structure.

Potential deviations from linear dispersion relations in quantum field theory.

Abstract

The canonical operator $\hat{a}^{\dagger}$ ($\hat{a}$) represents the ideal process of adding (subtracting) an {\it exact} amount of energy $E$ to (from) a physical system in both elementary quantum mechanics and quantum field theory. This is a ``sharp'' notion in the sense that no variability around $E$ is possible at the operator level. In this work, we present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.