A gauge structure hidden in the fundamental algebra for quantum mechanics on S(D)

Yoshio Ohnuki

Uwe Günther, Sergiusz Kużel

Gauged PT quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan decompositions. A Lie triple structure is found and an interpretation as PT-symmetrically generalized Jaynes-Cummings model is possible with close relation to recently studied cavity QED setups with transmon states in multilevel artificial atoms. For models with Abelian gauge potentials a hidden Clifford algebra structure is found and used to obtain the fundamental symmetry of Krein space related J-selfadjoint extensions for PTQM setups with ultra-localized potentials.

Yuval Ne’eman

Jincheng Zhang

This paper investigates the potential of quantum mechanics to induce emergent symmetry in abstract algebraic structures, offering a novel approach to understanding fundamental group theory and related areas. We explore the concept of quantum entanglement as a mechanism for creating a 'quantum resonance' between algebraic objects, suggesting a pathway to uncover previously hidden symmetries within these structures. The paper presents a theoretical framework and preliminary analysis, demonstrating a potential shift in perspective from traditional approaches to symmetry generation. We outline the core mechanism involving quantum entanglement and its implications for the study of group theory.

Yuval Ne’eman

Sumiyoshi Abe, Tsunehiro Kobayashi

Microcanonical ensemble theory of free bosons is derived from quantum mechanics by making use of the hidden gauge structure. The relative phase interaction associated with this gauge structure, described by the Pegg-Barnett formalism, is shown to lead to perfect decoherence in the thermodynamic limit and the principle of equal a priori probability, simultaneously.