An Algebraic Approach to Light–Matter Interactions

A theoretical and computational framework for the study and engineering of light–matter interactions is reviewed in here. The framework rests on the invariance properties of electromagnetism, and is formalized in a Hilbert space whose conformally invariant scalar product provides connections to phys...

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Published inAdvanced Physics Research Vol. 4; no. 1
Main Author Fernandez‐Corbaton, Ivan
Format Journal Article
LanguageEnglish
Published Edinburgh John Wiley & Sons, Inc 01.01.2025
Wiley-VCH
Subjects
Algebra
conformal symmetry
Electromagnetism
Hilbert space
Light
light–matter interactions
Operators (mathematics)
Physics
Spacetime
Symmetry
Theoretical physics
Theory of relativity
T‐matrix
Online AccessGet full text
ISSN2751-1200
2751-1200
DOI10.1002/apxr.202400088

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Abstract A theoretical and computational framework for the study and engineering of light–matter interactions is reviewed in here. The framework rests on the invariance properties of electromagnetism, and is formalized in a Hilbert space whose conformally invariant scalar product provides connections to physical quantities, such as the energy or momentum of a given field, or the outcome of measurements. The light–matter interaction is modeled by the polychromatic scattering operator, which establishes a natural connection to a popular computational formalism, the transition matrix, or T‐matrix. This review contains a succinct yet comprehensive description of the main theoretical ideas, and illustrates some of the practical benefits of the approach. This is a review of an algebraic approach to light–matter interactions that is theoretically powerful and computationally friendly. Theoretical expressions can be developed and manipulated conveniently thanks to the generality of the basis on which the approach rests, and a compact notation. The tight connections to popular computational tools allow one to readily perform numerical calculations.
AbstractList Abstract A theoretical and computational framework for the study and engineering of light–matter interactions is reviewed in here. The framework rests on the invariance properties of electromagnetism, and is formalized in a Hilbert space whose conformally invariant scalar product provides connections to physical quantities, such as the energy or momentum of a given field, or the outcome of measurements. The light–matter interaction is modeled by the polychromatic scattering operator, which establishes a natural connection to a popular computational formalism, the transition matrix, or T‐matrix. This review contains a succinct yet comprehensive description of the main theoretical ideas, and illustrates some of the practical benefits of the approach.
A theoretical and computational framework for the study and engineering of light–matter interactions is reviewed in here. The framework rests on the invariance properties of electromagnetism, and is formalized in a Hilbert space whose conformally invariant scalar product provides connections to physical quantities, such as the energy or momentum of a given field, or the outcome of measurements. The light–matter interaction is modeled by the polychromatic scattering operator, which establishes a natural connection to a popular computational formalism, the transition matrix, or T‐matrix. This review contains a succinct yet comprehensive description of the main theoretical ideas, and illustrates some of the practical benefits of the approach.
A theoretical and computational framework for the study and engineering of light–matter interactions is reviewed in here. The framework rests on the invariance properties of electromagnetism, and is formalized in a Hilbert space whose conformally invariant scalar product provides connections to physical quantities, such as the energy or momentum of a given field, or the outcome of measurements. The light–matter interaction is modeled by the polychromatic scattering operator, which establishes a natural connection to a popular computational formalism, the transition matrix, or T‐matrix. This review contains a succinct yet comprehensive description of the main theoretical ideas, and illustrates some of the practical benefits of the approach.
A theoretical and computational framework for the study and engineering of light–matter interactions is reviewed in here. The framework rests on the invariance properties of electromagnetism, and is formalized in a Hilbert space whose conformally invariant scalar product provides connections to physical quantities, such as the energy or momentum of a given field, or the outcome of measurements. The light–matter interaction is modeled by the polychromatic scattering operator, which establishes a natural connection to a popular computational formalism, the transition matrix, or T‐matrix. This review contains a succinct yet comprehensive description of the main theoretical ideas, and illustrates some of the practical benefits of the approach. This is a review of an algebraic approach to light–matter interactions that is theoretically powerful and computationally friendly. Theoretical expressions can be developed and manipulated conveniently thanks to the generality of the basis on which the approach rests, and a compact notation. The tight connections to popular computational tools allow one to readily perform numerical calculations.
Author Fernandez‐Corbaton, Ivan
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  fullname: Fernandez‐Corbaton, Ivan
  email: ivan.fernandez-corbaton@kit.edu
  organization: Karlsruhe Institute of Technology
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Snippet A theoretical and computational framework for the study and engineering of light–matter interactions is reviewed in here. The framework rests on the invariance...
Abstract A theoretical and computational framework for the study and engineering of light–matter interactions is reviewed in here. The framework rests on the...
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SubjectTerms Algebra
conformal symmetry
Electromagnetism
Hilbert space
Light
light–matter interactions
Operators (mathematics)
Physics
Spacetime
Symmetry
Theoretical physics
Theory of relativity
T‐matrix
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Title An Algebraic Approach to Light–Matter Interactions
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Volume 4
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