Quantum collective field and correction

Michael Laskin, Tankut Can, Paul B. Wiegmann

We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian field theory arise from the covariant ultraviolet regularization of the theory, which produces the gravitational anomaly. These corrections are described by a theory closely related to the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.

Hagen M. Kleinert

Abdelmalek Bouzenada

We investigate the collective spontaneous emission of ordered atomic arrays in the presence of external magnetic fields and generalized gravitational backgrounds. In this case, within a unified theoretical framework, the influence of magnetic interactions in cooperative radiative processes is analyzed through modified transition dynamics and collective coupling effects between interacting atoms. Also, the formalism includes generalized gravitational contributions to the emission process, permitting the evaluation of curvature-dependent phase corrections and their combined influence with magnetic-field interactions. Moreover, the collective emission spectrum is obtained through an eikonal reduction procedure, where both the gravitational phase and magnetic coupling modify the spectral profile and coherence characteristics of the emitted radiation. In addition, the many-body transition amplitude and generalized structure factor are constructed to describe cooperative quantum interference and correlation effects in interacting atomic configurations. In this case, the results demonstrate that external magnetic fields and gravitational backgrounds generate observable corrections in collective decay channels, spectral line profiles, and coherence properties within atomic arrays. In this context, these results establish a generalized formulation of cooperative quantum emission in environments where electromagnetic and gravitational interactions coexist, with applications to quantum optics, precision spectroscopy, relativistic quantum systems, and field-dependent collective atomic platforms.

Eduardo C. Marino

Hagen M. Kleinert

C. M. Bowden, F. A. Hopf, W. H. Louisell

The local field correction (LFC) is associated with the passage from microscopic to macroscopic electrodynamics. The conventional derivation of the LFC is found in Jackson1, and the implication is that the correction is due to all of the atoms in the system, which implies some kind of collective phenomenon. In the work reported here, we draw heavily upon the discussion of the LFC of Van Kranendank and Sipe2 (KS).