Foundations of Many-Body Theory of Quantum Unified Statistics: Green functions and Linear Response Theory
Abstract
We develop a comprehensive many-body theory for systems of particles obeying quantum unified statistics, or quons. After exploring the properties of the Fock space of this system, we formulate a systematic S-matrix expansion and a generalized Wick's theorem. A consistent Green-function formalism is constructed at both zero and finite temperatures, accompanied by a generalized Wick's theorem appropriate for infinite-statistics operator algebras. Within this framework, we establish diagrammatic rules for interacting quon systems. Employing the random phase approximation, we derive the dielectric function and reveal the emergence of anomalous plasmon modes that have no direct counterpart in conventional Bose or Fermi systems. We further analyze the ground-state energy, energy-loss function, generalized Thomas-Fermi screening wave vectors, and Friedel oscillations, elucidating how infinite statistics qualitatively modifies collective behavior and screening properties.
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BibTeX
@misc{beyrami2026foundations,
title = {{Foundations of Many-Body Theory of Quantum Unified Statistics: Green functions and Linear Response Theory}},
author = {M. Beyrami and M. N. Najafi and H. Esmaili and M. Dournama and H. Mohammadzadeh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05878},
eprint = {2609.05878},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05878},
}
RIS
TY - UNPB
TI - Foundations of Many-Body Theory of Quantum Unified Statistics: Green functions and Linear Response Theory
AU - M. Beyrami
AU - M. N. Najafi
AU - H. Esmaili
AU - M. Dournama
AU - H. Mohammadzadeh
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.05878
UR - https://arxiv.org/abs/2609.05878
AB - We develop a comprehensive many-body theory for systems of particles obeying quantum unified statistics, or quons. After exploring the properties of the Fock space of this system, we formulate a systematic S-matrix expansion and a generalized Wick's theorem. A consistent Green-function formalism is constructed at both zero and finite temperatures, accompanied by a generalized Wick's theorem appropriate for infinite-statistics operator algebras. Within this framework, we establish diagrammatic rules for interacting quon systems. Employing the random phase approximation, we derive the dielectric function and reveal the emergence of anomalous plasmon modes that have no direct counterpart in conventional Bose or Fermi systems. We further analyze the ground-state energy, energy-loss function, generalized Thomas-Fermi screening wave vectors, and Friedel oscillations, elucidating how infinite statistics qualitatively modifies collective behavior and screening properties.
ER -