Rigged Hilbert Space formulation for quasi-Hermitian composite systems

• URL: http://arxiv.org/abs/2405.02848v2
• Date: Thu, 19 Dec 2024 04:20:06 GMT
• Title: Rigged Hilbert Space formulation for quasi-Hermitian composite systems
• Abstract summary: Dirac's bra-ket formalism is used to construct the bra and ket vectors for a non-Hermite composite system.<n>We show that the symmetric relations regarding quasi-Hermitian operators can be extended to dual spaces.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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