Rigged Hilbert Space formulation for quasi-Hermitian composite systems
Abstract
The discussion in this study delves into Dirac's bra-ket formalism for a quasi-Hermitian quantum composite system based on the rigged Hilbert space (RHS). We establish an RHS with a positive definite metric suitable for a quasi-Hermite composite system. The obtained RHS is utilized to construct the bra and ket vectors for the non-Hermite composite system and produce the spectral decomposition of the quasi-Hermitian operator. We show that the symmetric relations regarding quasi-Hermitian operators can be extended to dual spaces, and all descriptions obtained using the bra-ket formalism are completely developed in the dual spaces. Our methodology is applied to a non-Hermitian harmonic oscillator composed of conformal multi-dimensional many-body systems.
Keywords
Cite
@article{arxiv.2405.02848,
title = {Rigged Hilbert Space formulation for quasi-Hermitian composite systems},
author = {Shousuke Ohmori},
journal= {arXiv preprint arXiv:2405.02848},
year = {2024}
}