# Extending bosons and fermions beyond pairwise exchange symmetry

## TL;DR

This paper introduces immanons, hypothetical particles that generalize bosons and fermions by obeying exchange symmetries beyond pairwise interactions, leading to new quantum statistical behaviors and a partial Pauli principle.

## Contribution

It extends the concept of exchange symmetry to particles beyond bosons and fermions, defining immanons and exploring their quantum properties and measurable consequences.

## Key findings

- Immanons obey a partial Pauli principle limiting occupation numbers.
- The scalar product of many-body states is given by the immanant of a matrix.
- A Gedankenexperiment supports the permanental dominance conjecture.

## Abstract

We study quantum many-body states of immanons, hypothetical particles that obey an exchange symmetry defined for more than two participating particles. Immanons thereby generalize bosons and fermions, which are defined by their behavior under pairwise symmetric and anti-symmetric exchange processes. The scalar product of two many-body states with fermionic, bosonic or generalized exchange symmetry becomes the determinant, permanent or immanant of the matrix containing all mutual scalar products of the occupied single-particle states. As a measurable consequence, immanons are shown to obey a partial Pauli principle that forbids the multiple occupation of single-particle states above a certain threshold. The tendency to favor or oppose multiple occupation of single-particle modes, i.e. the degree of bunching, is the determinant, permanent or immanant of a hermitian positive semi-definite matrix. We exploit this identity to devise a Gedankenexperiment that corroborates the permanental dominance conjecture.