Comparing Hermitian and Non-Hermitian Quantum Electrodynamics

In recent years, non-Hermitian quantum physics has gained a great deal of 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...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 14; no. 9; p. 1816
Main Authors Southall, Jake, Hodgson, Daniel, Purdy, Robert, Beige, Almut
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2022
Subjects
Bosons
Commutators
Electromagnetic fields
Energy
Light
Magnetic fields
non-Hermitian quantum physics
Optics
Propagation
Quantum electrodynamics
Quantum field theory
Quantum optics
Quantum physics
Quantum theory
Symmetry
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Summary:In recent years, non-Hermitian quantum physics has gained a great deal of 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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14091816