Correlation operators in many-particle physics

Jean-Louis Basdevant, Jean Dalibard

Corbin Pacheco, Nausheen R. Shah

In this article we explore ideas from quantum entanglement which can be meaningfully formulated and tested in the collider environment. We propose Bell-type inequalities as operator-level diagnostics of quantum incompatibility in particle-physics systems. We construct flavor operators associated with mass identification, flavor change, and charged-current weak mixing which arise from fundamental interactions in the Standard Model. We treat these interactions as alternative measurement settings in a Gendanken experiment. For entangled two-particle states, these operators generate nontrivial correlations that violate Bell-type bounds, excluding non-contextual local descriptions under the stated assumptions. These violations arise from the algebraic structure of the operators rather than from kinematic correlations or exotic dynamics. We discuss how the predicted correlation patterns may be probed with experimental data, clarifying the scope and limitations of Bell-type reasoning in particle physics.

Jørgen Rammer

Hideki Matsumoto

Since the discovery of high Tc superconductors in cuprate oxides, physics of highly correlated electron systems has become one of the central issues in condensed matter physics. We can find many examples of highly correlated particle systems not only in electron systems, such as high Tc superconductors and transition metal oxides, but also in bosonic systems, such as alkaline atomic gases in an optical lattice and mesoscopic Josephson junction arrays. In this lecture, we illustrate several models of highly correlated particle systems of fermionic and bosonic systems, and clarify common features of these systems. Then theoretical approaches to analyze these systems will be reviewed; special emphasis is on the composite operator method, which has been developed by the present author and the Salerno group.

A.I. Steshenko

A quantum mechanical model for a system of interacting bodies, taking into account noncommutativity of the coordinate and impulse operators for different particles and also the correlation equalities, is considered. The noncommutativity of the operators is here the result of the action of interparticle forces and represents natural generalization of the conventional commutation relation between the coordinate and impulse operators for a single particle. The efficiency of the model is evidenced by the specific calculations of well-known systems of atomic physics.