Generalized boson and fermion operators with a maximal total occupation property

TL;DR

This paper introduces a generalized algebra for boson and fermion operators that limits the total occupation number to a maximum value p, extending traditional quantum statistics with a new fractional coefficient framework.

Contribution

It presents a novel generalization of (anti-)commutation relations that constrains total occupation number, linking group theory with particle statistics.

Findings

New fractional coefficient relations for creation and annihilation operators.

Maximum total occupation number p in the Fock space.

Established correspondence with known particle statistics.

Abstract

We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard (anti-)commutator relation involving one creation and one annihilation operator is deformed by introducing fractional coefficients, containing a positive integer parameter $p$. The Fock space is determined by the classical definition. The new relations are chosen in such a way that the total occupation number in the system has the maximum value $p$. From the actions of creation and annihilation operators in the Fock space, a group theoretical framework is determined, and from here the correspondence with known particle statistics is established.