Comparing Hermitian and Non-Hermitian Quantum Electrodynamics

• URL: http://arxiv.org/abs/2208.01532v1
• Date: Tue, 2 Aug 2022 15:31:55 GMT
• Title: Comparing Hermitian and Non-Hermitian Quantum Electrodynamics
• Authors: Jake Southall, Daniel Hodgson, Robert Purdy and Almut Beige
• Abstract summary: In recent years, non-Hermitian quantum physics has gained a lot in popularity in the quantum optics and condensed matter communities. In this paper, we identify a non-standard inner product that implies bosonic commutator relations for local electric and magnetic field observables. We find that there is an equivalence between the two approaches.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In recent years, non-Hermitian quantum physics has gained a lot in popularity in the quantum optics and condensed matter communities in order to model quantum systems with varying symmetries. In this paper, we identify a non-standard inner product that implies bosonic commutator relations for local electric and magnetic field observables and leads to a natural local biorthogonal description of the quantised electromagnetic field. When comparing this description with an alternative local Hermitian description, in which the states of local photonic particles - i.e. of so-called bosons localised in position (blips) - are orthogonal under the conventional Hermitian inner product, we find that there is an equivalence between the two approaches. Careful consideration needs to be given to the physical interpretation of the different descriptions. Whether a Hermitian or a non-Hermitian approach is more suitable depends on the circumstances that we want to model.

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